Difference between revisions of "Assignment 9 Overview"

From Course Wiki
Jump to: navigation, search
(Assignment details)
 
(9 intermediate revisions by 2 users not shown)
Line 3: Line 3:
 
[[Category:Optical Microscopy Lab]]
 
[[Category:Optical Microscopy Lab]]
 
{{Template:20.309}}
 
{{Template:20.309}}
 
 
__NOTOC__
 
__NOTOC__
 
 
==Introduction==
 
==Introduction==
  
Line 21: Line 19:
 
* binding kinetics of the dye
 
* binding kinetics of the dye
  
The goal for Assignment 9 is to write a model for ''V<sub>f,measured</sub>'' that takes these effects into account and use nonlinear regression to estimate the parameters of this function. The model proposed here adheres to Dr. [http://en.wikiquote.org/wiki/George_E._P._Box George E. P. Box's excellent advice] on modeling, in that it is both wrong and useful. Some of the assumptions are more dubious than others. The following reading will guide you through the concepts behind the model which will be useful when you sit down to write your code.
+
The goal for Assignment 9 is to write a model for ''V<sub>f,measured</sub>'' that takes these effects into account and use nonlinear regression to estimate the parameters of this function. The model proposed here adheres to Dr. [http://en.wikiquote.org/wiki/George_E._P._Box George E. P. Box's excellent advice] on modeling, in that it is both wrong and useful. Some of the assumptions are more dubious than others. You might ask: "why don't we just fit the DNA melting curve to a higher order polynomial?" - great question. We are developing a ''mechanistic model'', which means that we hope the fit parameters will give us some insight into the physical processes behind the DNA melting system. Fitting an arbitrary function may be useful to interpolate the data, but provides no physical insights.
  
 +
Onward!
  
==Finding double stranded DNA fraction from raw data==
+
==Assignment details==
[[Image:Corrected DNA data.png|thumb|right]]
+
  
The inverse function of the melting model with respect to ''V<sub>f,measured</sub>''(''t'') is helpful to visualize discrepancies between the model and experimental data caused by random noise in ''V<sub>f,measured</sub>'' and systematic error in the model ''V<sub>f,model''. The function,
+
In this assignment you will write the code to analyze your DNA melting data in three parts:
 +
# In Part 1, [[Assignment 9, Part 1: model function|you will define the functions for each phenomenon and combine them into a single fit function]];
 +
# In Part 2, [[Assignment 9, Part 2: Simulating DNA melting data and testing the model function|you will create some simulated data to verify your code and test your model]].
 +
# In Part 3, [[Assignment 9, Part 3: Fitting your data| you will use the code on your real data and think about the statistical model you'll use to identify your unknown sample]].
  
::<math>C_{ds,inverse-model}(V_{f,measured}(t)) = \frac{V_{f,measured}(t) - K_{offset}} {K_{gain} S(t) Q(t)}</math>,
 
  
is itself a model. This model estimates the concentration of double stranded DNA based on the observations <math>V_{f,measured}(t)</math> and the models for bleaching and quenching.  
+
{| cellpadding="5" style="background:#FFCCCC; border:2px dashed #ff0000"
 +
|-
 +
|Warning: you will need the code written in this assignment to analyze your data in Assignment 10. Drop at your own risk!!
 +
|}
  
The estimated melting curve may be directly compared with simulations, measurements or other predictions of the true melting curve. The plot at right shows an example of ''C<sub>ds,inverse-model</sub>''(''t'') versus ''T<sub>sample</sub>''(''t''). The estimated melting curve is shifted to the right compared to the simulated melting curve, possibly due to systematic error in the sample temperature model. The estimated melting curve also serves as a comparison to the thermodynamic model developed in [[DNA Melting Thermodynamics]], or to any other independent measurement or model of the melting curve, i.e., the concentration of dsDNA vs sample temperature.
+
{{Template:Assignment Turn In|message=Turn in all of your work (comprehensive list below) on Stellar in a single PDF file named <lastname><firstname>Assignment9.pdf.
 
+
==Assignment details==
+
 
+
In this assignment you will write the code to analyze your DNA melting data in two parts:
+
# In Part 1, [[Assignment 9, Part 1: model function|you will define the functions for each phenomenon and combine them into a single fit function]];
+
# In Part 2, [[Assignment 9, Part 2: Simulating DNA melting data and testing the model function|you will create some simulated data to verify your code and test your model]].
+
  
{{Template:Assignment Turn In|message=Turn in all of your work (comprehensive list below) on Stellar in a single PDF file named <lastname><firstname>Assignment9.pdf.}}
+
Part 1: ('''individually''')
Turn in:
+
* Turn in your code for SimulateLowPass, SimulatePhotobleaching, SimulateThermalQuenching and Vmodel (once it has been tested!)
 +
Part 2: ('''individually''')
 +
* Plot the following items on the same set of axes. Don't forget to include a legend!
 +
*# your simulated fluorescence data as a function of block temperature
 +
*# your model function with initial best-guess parameters as a function of block temperature
 +
*# your model function with fitted par meters (obtained by nlinfit) as a function of block temperature
 +
* Calculate the uncertainty for each parameter from the fit, and fill in the uncertainty table, making sure to include appropriate units and significant figures.
 +
* Plot the normalized uncertainty for each fit parameter as a function of the noise magnitude. Which parameter appears to be the most sensitive to noise? the least?
 +
* Using the expressions we derived in class for [[DNA Melting Thermodynamics#Simulating DNA Melting|dsDNA concentration at a given temperature]], derive an expression for the melting temperature, <math>T_m</math>in terms of <math>\Delta H </math> and <math>\Delta S</math>. The melting temperature is defined as the temperature for which the fraction of double stranded DNA equals 0.5. Calculate the melting temperature for each noise level from 0.01 to 0.05.
 +
Part 3: ('''individually''')
 +
*# Plot your fluorescence data as a function of block 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. Calculate T<sub>m</sub>.
 +
*# How do these thermodynamic parameters compare to the predicted values you obtained from DINAmelt or OligoCalc?
 +
* For one fit result, plot the residuals vs.
 +
*# time,
 +
*# temperature, and
 +
*# fluorescence.
 +
* Write a function to convert fluorescence into fraction of double stranded DNA. For at least one experimental trial, plot <math>\text{DnaFraction}_{inverse-model}</math> versus the ''sample temperature'' <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.
 +
* Explain the statistical method you will use to identify your group's unknown sample in Assignment 10.
 +
*# State the acceptance/rejection criteria for any hypotheses tests you will use.
 +
*# This page may be a helpful reference: [[Identifying the unknown DNA sample]].
 +
Finally,
 +
*Append all of the code (not yet included) that you wrote for Parts 1, 2 and 3 of this assignment.
 +
}}
  
 
{{Template:Assignment 9 navigation}}
 
{{Template:Assignment 9 navigation}}

Latest revision as of 00:20, 25 January 2018

20.309: Biological Instrumentation and Measurement

ImageBar 774.jpg


Introduction

Measured photodiode voltage, Vf,measured plotted versus block temperature, θblock along with model photodiode voltage, Vf,model.

In Assignment 8, you made some improvements to your DNA melting instrument, and (hopefully) collected some spectacular data. This assignment will focus on extracting useful information from the data in order to make some quantitative conclusions.

The fluorescence voltage, Vf,measured(t), that you measured in lab depends not only on the parameters of interest, ΔH°, and ΔS°, but also on:

  • the double stranded DNA concentration Cds(t) (which we know from the outset)
  • the dynamics of the temperature cycling system
  • thermal quenching of the fluorophore
  • photobleaching
  • responsivity and offset of the instrument
  • binding kinetics of the dye

The goal for Assignment 9 is to write a model for Vf,measured that takes these effects into account and use nonlinear regression to estimate the parameters of this function. The model proposed here adheres to Dr. George E. P. Box's excellent advice on modeling, in that it is both wrong and useful. Some of the assumptions are more dubious than others. You might ask: "why don't we just fit the DNA melting curve to a higher order polynomial?" - great question. We are developing a mechanistic model, which means that we hope the fit parameters will give us some insight into the physical processes behind the DNA melting system. Fitting an arbitrary function may be useful to interpolate the data, but provides no physical insights.

Onward!

Assignment details

In this assignment you will write the code to analyze your DNA melting data in three parts:

  1. In Part 1, you will define the functions for each phenomenon and combine them into a single fit function;
  2. In Part 2, you will create some simulated data to verify your code and test your model.
  3. In Part 3, you will use the code on your real data and think about the statistical model you'll use to identify your unknown sample.


Warning: you will need the code written in this assignment to analyze your data in Assignment 10. Drop at your own risk!!


Pencil.png

Turn in all of your work (comprehensive list below) on Stellar in a single PDF file named <lastname><firstname>Assignment9.pdf.

Part 1: (individually)

  • Turn in your code for SimulateLowPass, SimulatePhotobleaching, SimulateThermalQuenching and Vmodel (once it has been tested!)

Part 2: (individually)

  • Plot the following items on the same set of axes. Don't forget to include a legend!
    1. your simulated fluorescence data as a function of block temperature
    2. your model function with initial best-guess parameters as a function of block temperature
    3. your model function with fitted par meters (obtained by nlinfit) as a function of block temperature
  • Calculate the uncertainty for each parameter from the fit, and fill in the uncertainty table, making sure to include appropriate units and significant figures.
  • Plot the normalized uncertainty for each fit parameter as a function of the noise magnitude. Which parameter appears to be the most sensitive to noise? the least?
  • Using the expressions we derived in class for dsDNA concentration at a given temperature, derive an expression for the melting temperature, $ T_m $in terms of $ \Delta H $ and $ \Delta S $. The melting temperature is defined as the temperature for which the fraction of double stranded DNA equals 0.5. Calculate the melting temperature for each noise level from 0.01 to 0.05.

Part 3: (individually)

    1. Plot your fluorescence data as a function of block temperature, your model function with initial guesses, and your model function with best fit parameters on the same set of axes.
    2. Record your estimates for ΔH and ΔS. Calculate Tm.
    3. How do these thermodynamic parameters compare to the predicted values you obtained from DINAmelt or OligoCalc?
  • For one fit result, plot the residuals vs.
    1. time,
    2. temperature, and
    3. fluorescence.
  • Write a function to convert fluorescence into fraction of double stranded DNA. For at least one experimental trial, plot $ \text{DnaFraction}_{inverse-model} $ versus the sample temperature $ 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.
  • Explain the statistical method you will use to identify your group's unknown sample in Assignment 10.
    1. State the acceptance/rejection criteria for any hypotheses tests you will use.
    2. This page may be a helpful reference: Identifying the unknown DNA sample.

Finally,

  • Append all of the code (not yet included) that you wrote for Parts 1, 2 and 3 of this assignment.


Navigation

Back to 20.309 Main Page