Assignment 9, Part 3: Fitting your data

Congratulations! you should now have a working version of your analysis code.

Estimate model parameters for real data

Use your model function and nlinfit to estimate the parameters associated with a set of DNA melting data that you took using your instrument. (set from last week.

Plot your fluorescence data as a function of temperature, your model function with initial guesses, and your model function with best fit parameters on the same set of axes. Record your estimates for &Delta H and &Delta S (along with their uncertainties). Calculate Tm. How do these thermodynamic parameters compare to the predicted values you obtained from DINAmelt or OligoCalc?

Comparing the known and unknown samples

One possible way to compare the unknown sample to the three knowns is to use Matlab's anova and multcompare functions. Anova takes care of the difficulties that arise when comparing multiple sample means using Student's t-test. Read through this page: Identifying the unknown DNA sample, to learn about the statistics behind making multiple comparisons.

The following code creates a simulated set of melting temperatures for three known samples and one unknown. In the simulation, each sample was run three times. The samples have melting temperatures of 270, 272, and 274 degrees. The unknown sample has a melting temperature of 272 degrees. Random noise is added to the true mean values to generate simulated results. Try running the code with different values of noiseStandardDeviation.

% create simulated dataset
noiseStandardDeviation = 0.5;
meltingTemperature = [270 270 270 272 272 272 274 274 274 272 272 272]
      + noiseStandardDeviation * randn(1,12);
sampleName = {'20bp' '20bp' '20bp' '30bp' '30bp' '30bp' '40bp' '40bp' '40bp'
      'unknown' 'unknown' 'unknown'};

% compute anova statistics
[p, table, anovaStatistics] = anova1(meltingTemperature, sampleName);

% do the multiple comparison
[comparison means plotHandle groupNames] = multcompare(anovaStatistics);

Output of multcompare command.

The multcompare function generates a table of confidence intervals for each possible pair-wise comparison. You can use the table to determine whether the means of two samples are significantly different. Output of multcompare is shown at right. If your data has a lot of variation, you might have to use the options to reduce the confidence level. (Or there might not be a significant difference at all.) Note that multcompare has a default confidence level of 95% (alpha = 0.05). One way to assess how confident you are in your sample identification is by finding the lowest "alpha" value needed to identify your sample.

Consider devising a more sophisticated method that uses both the ΔH° and ΔS° values, instead.

Explain the statistical method you will use to identify your group's unknown sample in part 2 of this lab. State the acceptance/rejection criteria for any hypotheses tests you will use. This page may be a helpful reference: Identifying the unknown DNA sample.

Append all of the code you wrote for Parts 1, 2 and 3 of this assignment.

Navigation

• Assignment 9 Overview
• Part 1: model function
• Part 2: test your code with simulated data
• Part 3: fitting your data

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