DNA Melting: Simulating DNA Melting - Intermediate Topics

Overview

In the DNA Melting Lab, the raw data you will record consists of two voltages as they vary over time. In order to estimate the melting temperature, these raw voltages will have to be converted to a melting curve, which gives the fraction of dsDNA as a function of temperature. Tm can be estimated by taking the peak of the derivative of the melting curve.

Data analysis steps include:

1. Filter raw data to remove noise.
2. Transform RTD voltage to temperature.
3. Transform photodiode current to relative fluorescence.
4. Ensure that the melting function is uniquely values by combining samples with identical temperature values.
5. Differentiate the resulting function.

It will be essential to have your data analysis scripts working before you come to the lab. This tutorial will demonstrate how to simulate a dataset for a DNA melting experiment. You can use the simulated data to help develop data analysis scripts.

Before you begin

• If you are need a review of Matlab fundamentals, see Matlab:Matlab Fundamentals
• Read the DNA Melting Lab Manual.
• You may also find it helpful to review the DNA Melting Thermodynamics Lecture Notes.

DNA melting lab data analysis

The steps are:

1. Filter raw data to remove noise.
2. Transform RTD voltage to temperature.
3. Transform photodiode current to relative fluorescence.
4. If necessary, combine multiple samples with identical temperature readings to ensure a uniquely valued function f(t).
5. Differentiate the resulting function.

Write a function to compute f

The first useful piece of code is a function that will compute $ \left . f \right . $ from the equation derived in class. This function must be in its own file called DnaFraction.m.

<include src="http://web.mit.edu/~20.309/www/Matlab/DnaFraction.m" />

The element-by-element divide operator (./) is used instead of the matrix divide operator(/) so that the temperature parameter T can be a vector. If T is a single value, both operators are equivalent. But the / operator will try to do a matrix divide if T is a vector or matrix and give an error since the dimension of the two operands do not match. A for...end loop could also be used to call DnaFraction once for each value of $ T $. But for loops have terrible performance in Matlab and your program will run much faster if you use a vector of $ T $ values instead.

%Returns the fraction of dsDNA given total DNA concentration, temperature, Delta S, and Delta H
%Usage: f = DnaFraction(Ct, T, DeltaS, DeltaH)
function f = DnaFraction(Ct, T, DeltaS, DeltaH)

%Constants
R=8.3;

%first compute Ct * Keq
CtKeq = Ct * exp(DeltaS / R - DeltaH / (R * T));

%now compute f
f = (1 + CtKeq + sqrt(1 + 2 * CtKeq))/CtKeq;

Test the function

First, create a temperature vector. Then call DnaFraction with some reasonable parameters and plot the result. Units are calorie, mole.

t = [20:90] + 273;
f = DnaFraction(.1E-6, t, 304E3, 786);
plot(t,f)