Difference between revisions of "Assignment 10 Overview"

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{{Template:Assignment Turn In|message=also your analysis:
 
{{Template:Assignment Turn In|message=also your analysis:
#* Use bullet points to explain your data analysis methodology.
+
* Use bullet points to explain your data analysis methodology.
#* Document the regression model you used to analyze your data
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* Document the regression model you used to analyze your data
#** See [[DNA Melting: Model function and parameter estimation by nonlinear regression]]
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** See [[DNA Melting: Model function and parameter estimation by nonlinear regression]]
#** Explain the model parameters using bullet points or in a table.
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** Explain the model parameters using bullet points or in a table.
#* Plot <math>V_{f,measured}</math> and <math>V_{f,model}</math> versus <math>T_{block}</math> for a typical run of each samples type. Use the smallest number of axes that clearly conveys the data.  
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* Plot <math>V_{f,measured}</math> and <math>V_{f,model}</math> versus <math>T_{block}</math> for a typical run of each samples type. Use the smallest number of axes that clearly conveys the data.  
#* For a typical curve, plot residuals versus time, temperature, and fluorescence, ([http://measurebiology.org/wiki/File:Residual_plot_for_DNA_data.png example plot]).
+
* For a typical curve, plot residuals versus time, temperature, and fluorescence, ([http://measurebiology.org/wiki/File:Residual_plot_for_DNA_data.png example plot]).
#* Provide a table of the best-fit model parameters and confidence intervals for each experimental run. Also include the estimated melting temperature for each run.
+
* Provide a table of the best-fit model parameters and confidence intervals for each experimental run. Also include the estimated melting temperature for each run.
#* For at least one experimental trial, plot <math>\text{DnaFraction}_{inverse-model}</math> versus <math>T_{sample}</math> ([http://measurebiology.org/wiki/File:Inverse_cuvrve.png example plot]). On the same set of axes plot DnaFraction versus <math>T_{sample}</math> using the best-fit values of &Delta;H and &Delta;S. Finally, plot simulated dsDNA fraction vs. temperature using data from DINAmelt or another melting curve simulator.
+
* For at least one experimental trial, plot <math>\text{DnaFraction}_{inverse-model}</math> versus <math>T_{sample}</math> ([http://measurebiology.org/wiki/File:Inverse_cuvrve.png example plot]). On the same set of axes plot DnaFraction versus <math>T_{sample}</math> using the best-fit values of &Delta;H and &Delta;S. Finally, plot simulated dsDNA fraction vs. temperature using data from DINAmelt or another melting curve simulator.
 
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Revision as of 18:31, 1 November 2017

20.309: Biological Instrumentation and Measurement

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Assignment 10

Data acquisition

Identify unknown sample

You will receive 1.5 mL each of four samples. Three of the samples will be identified by their sequence, salt ion concentration, and degree of complementarity (see these DNA_Melting:_DNA_Sequences). The fourth sample matches one of the three identified samples. You will not be told which one.

  • Acquire melting curves for the known and unknown samples.
    • You may want to run some or all of the samples more than once to provide more confidence in your result.
  • Identify the unknown sample and report your confidence in the result.
    • See Identifying the unknown DNA sample for some ideas on identifying the sample.
    • You may use a different statistical procedure, if you like. Be sure to document the procedure you used.


Pencil.png

Turn in your

  1. Procedure:
    • Document procedure used to gather data
  2. Raw data:
    • Measure melting curves 3x each of four samples (three known, one unknown). Plot all raw data.
  3. Results:
    • Identify your unknown sample (or state that your investigation did not provide a conclusive answer).
    • Quantify the confidence you have in your result.
  4. Discussion:
    • Discuss the validity of assumptions in the regression model.
    • Discuss any atypical results or data you rejected.
    • Compare your data to results from other groups and/or instructor data.
    • Give a bullet point summary of problems you encountered in the lab during part 2 and changes that you made to your instrument and methodology to address those issues.
    • Discuss significant error sources.
      • Consider the entire system: the oligos, dye, the experimental method, and analysis methodology, and any other relevant factors.
      • Indicate whether each source likely caused a systematic or random distortion in the data.
      • Present error sources, error type and their resultant uncertainty on your data and results in a table, if you like.
    • Discuss additional unimplemented changes that might improve your instrument or analysis.


Analysis

We set out to measure the fraction of dsDNA versus temperature. As discussed in lecture, factors like photobleaching, thermal quenching, and the difference between the block and sample temperature distorted the measurement in various ways. For the final report, you will carefully analyze your data using a mechanistic model to factor out the melting dynamics from the shortcomings of the measurement technique.

In an ideal world, you would have your analysis code written before the data is collected. In the real world, data collection involves a lot of waiting around, and it might be a good use of your time to work on the analysis code and collect data in parallel. In that case, it is still important to ensure that your data makes sense as it comes in. For example, is the trend in the melting temperature what you expected? … e.g. did longer oligos have a higher melting temperature than shorter ones? The following section provides a quick way to estimate melting temperatures from the raw data.

Estimating melting temperatures from raw data

Vf / ∂ T versus T

A frequently-used, quick-and-dirty proxy for melting temperature is the peak value of the fluorescence voltage's derivative as a function of temperature. The peak of the derivative is the temperature at which the equilibrium is changing most rapidly. It's not exactly the same as the melting temperature, but it allows for quick comparison of results.

You can't just take the derivative of the raw signal. The raw data is not guaranteed to be a function at all. One way to take a good derivative is to combine the fluorescence voltage values that fall into a particular range of temperatures and then take the average of all those values — a process sometimes called binning or discretization. Temperature bins of about a quarter of a degree work well. The code below demonstrates how to accomplish this in MATLAB. Because of the difference between the block and sample temperatures, it is best to do this for just the heating or melting portion of the curve.

Assuming the variables temperature and fluorescence are defined, the following Matlab code fragment below computes ΔF/ΔT for the heating portion of the curve. If your melting curves are very noisy, you may have to adjust the code.

discretizationInterval = 0.25;
discreteTemperatureAxis = 20: discretizationInterval:100; % center value for each bin
discreteTemperaturBinEdges = [ discreteTemperatureAxis - discretizationInterval / 2, 
      discreteTemperatureAxis(end) + discretizationInterval / 2 ];
temperatureBinIndex = discretize( temperature, discreteTemperaturBinEdges );
binnedFluorescence = accumarray( temperatureBinIndex', fluorescence', 
      size( discreteTemperatureAxis' ), @mean )';
badOnes = binnedFluorescence == 0;
discreteTemperatureAxis( badOnes ) = [];
binnedFluorescence( badOnes ) = [];

figure
subplot(211)
plot( discreteTemperatureAxis, binnedFluorescence )
title( 'Average Fluorescence Voltage versus Temperature')
xlabel( 'T (^{\circ}C)' )
ylabel( 'F (AU)' )

dFluorescenceDTemperature =  diff( binnedFluorescence ) ./ diff( discreteTemperatureAxis );
derivativeAxis = mean( [ discreteTemperatureAxis(1:(end-1)); discreteTemperatureAxis(2:end) ] );

subplot(212)
plot( derivativeAxis, dFluorescenceDTemperature);
title( 'Derivative of Fluorescence versus Temperature' )
xlabel( 'T (^{\circ}C)' )
ylabel( 'dF/dT' )

Using nonlinear regression to estimate parameters

The DNA Melting: Model function and parameter estimation by nonlinear regression wiki page will guide you in writing the model function used to estimate the relevant DNA melting parameters.


Pencil.png

Turn in the opening of a lab report:

  1. Haiku:
    • Compose an entertaining, exhilarating, thought-provoking, or melancholy Haiku on the subject of DNA melting.
  2. Abstract:
    • In one paragraph containing six or fewer sentences, summarize the investigation you undertook and key results.
  3. Introduction and Purpose:
    • Provide a succinct introduction to the project, including the purpose of the experiment, relevant background material and/or links to such information.
    • Summarize the ways in which this part of the lab differs from Part 1 covered in Assignment 7.
    • Keep the length to one or two short paragraphs, no more than 1/3 of a page.



Pencil.png

also your analysis:

  • Use bullet points to explain your data analysis methodology.
  • Document the regression model you used to analyze your data
  • Plot $ V_{f,measured} $ and $ V_{f,model} $ versus $ T_{block} $ for a typical run of each samples type. Use the smallest number of axes that clearly conveys the data.
  • For a typical curve, plot residuals versus time, temperature, and fluorescence, (example plot).
  • Provide a table of the best-fit model parameters and confidence intervals for each experimental run. Also include the estimated melting temperature for each run.
  • For at least one experimental trial, plot $ \text{DnaFraction}_{inverse-model} $ versus $ T_{sample} $ (example plot). On the same set of axes plot DnaFraction versus $ T_{sample} $ using the best-fit values of ΔH and ΔS. Finally, plot simulated dsDNA fraction vs. temperature using data from DINAmelt or another melting curve simulator.


Resources

Background reading

Code examples and simulations

Subset of datasheets

(Many more can be found online or on the course share)

  1. National Instruments USB-6212 user manual
  2. National Instruments USB-6341 user manual
  3. LF411 Op-amp datasheet
  4. LM741 Op-amp datasheet


Navigation

Back to 20.309 Main Page