Assignment 9 Overview

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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. 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 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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