IMPORTANT: The numbers below are for an old sheet! Substitute appropriately for the new sheets! Also note that there are 2 versions of the mutarotation handout - one is for xylose, one is for glucose - which differ in their numbers (and may differ from the below). Substitute for 7.7 in the below as appropriate for the version that you have - 21 [This is new: not 21.2, which is what the sheet currently says, since that will leave the last point with a value of 0 after subtracting, which will be infinity for the log of it...] for the glucose data. [This is new: In at least the glucose data, there appears to be a typo with the optical rotation for time 15 minutes being 20 degrees. (As far as I know, there is no corresponding typo in the xylose data, which is why I'm thinking this is a typo and not a deliberate bad point.) You should delete this point.] NOTE: This is for SigmaPlot 4.01, the version on the (slow and crash-prone) PC in 118, my office. It should be pretty similar if someone has a later version of SigmaPlot, although moving files back and forth between different versions is likely to be problematic! I suspect saving in Excel format may do better. 1. Enter the time (in minutes) into column 1 2. Enter the optical rotation into column 2 3. Right-click on each column to label it ("Time" for column 1, "OR" for column 2); this step is actually optional, but it makes it easier to keep track when you have a lot of columns, and the info below on which column to select will be in terms of these labels. 4. Click on the menu bar on "Transforms" 5. Click on "User-Defined" in the menu it brings up. 6. In the box it now shows you, enter two lines: col(3)=col(2)-7.7 col(4)=ln(col(3)) The first line says that column 3 should have in it column 2 minus 7.7. The second line says that column 4 should have in it the natural log (ln) of column 3. Hit the "Execute" button. You should now label column 3 "OR-7.7" and column 4 "ln(OR-7.7)". [Note that the 7.7 may need changing!] 7. To get an exponential fit, first you should graph the points. Go to Graph, Create Graph, select a Scatter Plot, Simple Scatter, XY pair, make Time your X and OR-7.7 your Y. You should get a graph of the points. To fit a simple exponential curve to this, right-click on one of the points, and select "Fit Curve" from the menu that pops up. Select equation category "Exponential Decay", then - since Dr. Chase wants you to do an equation without a y0 - "Single, 2 parameter". Hit Next. The variables should be properly set already for what is X and what is Y (this is why - no pun intended! - I had you right-click on a point to get the "Regression Wizard", as opposed to going under the "Statistics" menu). Hit Next. The coefficients should now be shown, plus the R-squared (THIS SHOULD BE WHAT YOU USE WITH KALIDAGRAPH, NOT PLAIN R, AT LEAST IF YOU WANT ME TO HELP YOU WITH WHETHER YOUR GRAPH NEEDS POINTS TAKEN OUT! Changing this in Kalidagraph is done through the "Format" menu, via "Curve Fit format" or something like that) and some other information (e.g., if you tried using an equation with more parameters, you would look at the "Dependencies" column to see whether these were necessary - the closer to 1, the more the other parameters can handle the job of the parameter in question). Hit Next. Make sure "Report" is checked; you don't need "Add Equation to Notebook" and you don't need the Parameters, Predicted, or Residuals (remember the protein statistics?), so make sure they aren't checked. Hit Next. Selected should be "Add curve to" 2D Graph 1. That will add the curve to the graph you already have, which is what you want - again, this is why you right-clicked on a point on the graph above. [The following is a change: Hit Next. Make sure that beside "x column" and "y column" are "First Empty". Then hit Finish.] You will see a couple more columns of data added to your worksheet - this is the data on what points are being plotted. (The "First Empty" tells it to put these columns here, not on top of other columns.) You should also - more importantly - see a report on the curve-fitting, which will give you the parameters, errors, R-squared, adjusted R-squared, residuals, etcetera, etcetera (although let me - or Dr. Kahn if I'm not available - know if you ever do something with SigmaPlot and the "Tests" (Normality, Constant Variance, or whatever) are failed, unless you know already that you did something wrong and can work out how to do it the right way), and the line of the curve should now be on the graph. 8. You do the second graph the same way at the start, and it will look like the same set of points. (There is an annoying thing about SigmaPlot that it will plop the second graph on top of the first; just move them around so they're out of the way of each other. Or you can create a new page - see #9.) Now click on the graph, and in the menu it shows you, select Graph Properties. Go over to the Axes tab, select the Y data axis, and set the scale type to "Log (natural)". Hit OK. The graph should transform to a semilog plot, showing a (slightly curved) line. The axis is now in terms of powers of e; if Dr. Chase wants it as numbers, he should let you know before the lab report is due. Now do another Exponential Decay (Single, 2 parameter) plot. As Dr. Chase says, the results should be numerically the same as before. It's quite noticeable how the top portion of the graph is better fitted in the plot, however, unlike with a non-semilog plot. 9. You now want to do a graph of the "Time" column vs the "ln(OR-7.7)" column. To move the graph onto another page, go over to the box on the upper-left of the screen (unless you moved it), right-click on anything under "Section 1", select "New", and select "Graph Page". Tell it "no" when it asks if you want to create a graph, if you've already created the one you want to move. You can then move the graph over to the resulting page. Alternatively, just create a new graph page, answer "yes", _then_ create the graph (which appears to be what the designers intended). Right-click on one of the points, hit "Fit Curve", select equation category "Polynomial", then "Linear", then Next. Again, the variables should be right in the next screen, so hit Next. You should get the same sort of window as before, with R-squared et al. (I note the dependencies are less for this; interesting!) Go through the same thing as before to get the report, the line graphed, etcetera. Take a look at the Report values and at the graph to see how well it looks. 10. SigmaPlot has the equation that Dr. Chase has in Kalidagraph format for "plot #4" as a built-in equation. (When we get to plotting Michaelis-Menton equations for the Enzyme lab, I'll try to put up something on how to put in an equation, initial values, etcetera into SigmaPlot.) Plot the "Time" column vs the "OR" column (X vs Y), do "Fit Curve", equation category "Exponential Decay", equation "Single, 3 Parameter". Hit Next. The variables should again be set up properly, so hit Next again. You should see the same sort of screen with R-squared as before - but this time there are three parameters being fitted. (This tends to result in the Dependencies being higher, BTW.) Go through to get a report and a fitted curve. 11. I note in these that the slower rate of mutarotation at the start (probably because of the heat of the bulb warming the solution by the end) tends to result in a distortion of the rest of the curve, because of the lots of points close together at the start (small time intervals) - that means they tend to weigh more in the determination of the curve. I managed to get a closer fit with the following equation: y=y0+a*exp(-b*x)+c*x (in other words, OR = y0 + a*e^(-b*[time]) + c*[time]; this is an "Exponential Linear Combination") and these coefficients: Coefficient Std. Error t P a 43.2829 3.8074 11.3681 <0.0001 b 0.0435 0.0037 11.9129 <0.0001 c 0.1868 0.0518 3.6061 0.0026 y0 -6.1783 3.9369 -1.5693 0.1374 The y0 in the above has a problem with its P-value, and the Dependencies were pretty high, but aside from that, the above looks good. (Rsqr = 0.99936347 Adj Rsqr = 0.99923616). You aren't required to do this, and it'd be better to fix the problem with the initial experiment, but I got curious...