Difference between revisions of "Assignment 9 Overview"

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(Finding double stranded DNA fraction from raw data)
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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. The following reading will guide you through the concepts behind the model which will be useful when you sit down to write your code.
  
 
==Finding double stranded DNA fraction from raw data==
 
[[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,
 
 
::<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.
 
 
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.
 
  
 
==Assignment details==
 
==Assignment details==

Revision as of 00:49, 3 November 2017

20.309: Biological Instrumentation and Measurement

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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. The following reading will guide you through the concepts behind the model which will be useful when you sit down to write your code.


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 2, you will use the code on your real data and think about the statistical model you'll use to identify your unknown sample.



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


Turn in:

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