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Line/Curve of Best Fit?

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Line/Curve of Best Fit?

Postby vertciel » Thu Sep 11, 2008 1:06 pm

Hello everyone:

I have made a graph by hand for the Enzyme Lab in my AP Biology class, depicting the affect of pH on peroxidase activity. I graphed the rate of enzyme activity (1/s) versus the pH; the former is on the y-axis and the latter is on the x-axis. For reference, I have constructed the same graph on MS Excel as shown below.
[url]
http://img392.imageshack.us/my.php?image=graphai4.jpg[/url]

My coordinates are not linear or in a recognisable polynomial form, so I am wondering if I should draw a line of best fit, a curve of best fit, or connect all the points. I am also noticing that most of the time in biology and chemistry, a line or curve of best fit is chosen.

Thank you.

---
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Re: Line/Curve of Best Fit?

Postby blcr11 » Thu Sep 11, 2008 4:32 pm

The pH-activity profile for most enzymes is bell-shaped. There is a pH at which the velocity is maximal, and then activity falls off at pHs above or below the pH optimum. If you have enough points you could fit some sort of interpolating polynomial, but I don’t see how that would help you much. Maybe even Excel has a spline or interpolating function. A free-hand curve should do, I would think.

There are times when you need to "fit a line" by least squares regression or some such technique. If this were a Lineweaver-Burke plot that's exactly what you'd want to do, too. Or if this were a saturation binding curve, you'd be wanting to do a logit regression, maybe, or fit a sigmoidal model to the data--things like that. But here I think the curve is mostly descriptive. There really isn't an underlying model to fit the data to unless I misunderstand your description of the data.
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Postby alextemplet » Thu Sep 11, 2008 5:53 pm

It looks like a line originating from the zero point would cover the average of your points nicely. I would suggest a line of best fit, and if possible try to determine its algebraic formula.
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Postby mith » Thu Sep 11, 2008 6:23 pm

Oh it's pretty simple, deconstruct it as a summation of cosine curves.
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Postby blcr11 » Thu Sep 11, 2008 7:59 pm

Well, now I'm curious to know what the data actually looks like. I can't bring up the jpg at the moment--I'm blocked, not that there's anything wrong with the link. I'll have to try later this evening on another computer. I was assuming the plot looked at least a little like a bell curve, but maybe I'm wrong. Or maybe the pH optimum is something like pH 2 or 3 and all the data points are at pH 4 and above. Just a warning about curve fitting: if you have, say, 10 data points, you are guaranteed to find a 10th-degree polynomial that fits all the data points exactly--that is with residual errors of exactly zero. Just because it "fits" doesn't necessarily make it meaningful. Since Alex thinks a line through the origin might "fit" then I assume the data looks at least something like a line--which isn't what I would have expected, but there you have it. But it makes more sense to fit a line if it looks quasi linear than to go casting about for higher order polynomials, unless there is some mechanistic reason for it (like second order kinetics or some kind of apparent saturation phenomenon, etc.) I suspect you're going to need a few more data points if you're going to take mith's suggestion, which I also assume was meant to be tongue-in-cheek.
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Postby mith » Thu Sep 11, 2008 8:15 pm

Oh I was kidding, btw the graph looks like a proportional increase of activity as pH rises from 0-14. Not necessarily linear but definitely not bell shaped.
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Postby blcr11 » Thu Sep 11, 2008 10:59 pm

As it stands, the data looks either linear, quadratic, or sigmoidal/hyperbolic. But "here's a bet I'll bet youse" to steal a line from E. E. Cummings. I bet there is a mistake in the data points at pH 10 and 12. To check that, unfortunately, you're going to have to redo the entire set of experiments--or at least a few of the lower pHs and especially the pH 6-6.5 points. Perhaps your pH10 and pH12 points were left to incubate a little longer than the others or something like that. Are there replicates for each point? If so, you should show the error bars, too. The pH optimum for horseradish peroxidase is 6-6.5. There are other forms of peroxidase, but this one is the most commonly available reagent.
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Postby alextemplet » Fri Sep 12, 2008 4:29 pm

Really, any serious experiment should be repeated several times to make sure the results are accurate; however, if this for a class, then it depends on how advanced you are in your studies. At the high school level, a little innaccuracy in measurement is usually forgiven so long as you can demonstrate that you understand the process; in college and especially graduate school, you're usually expected to be as precise as possible.
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