The Kinetics of Polymerase Chain Reaction Product Duplex Dissociation

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BACKGROUND:

Polymerase Chain Reaction (PCR) is a biochemical reaction that amplifies DNA and is the cornerstone of modern molecular biology. A typical PCR reaction has three components: denaturation, annealing and extension. To optimize this reaction one must tinker with each of these steps to achieve maximum efficiency. Two of the reaction steps, extension and annealing, have been extensively studied. The speed of the denaturation reaction has been largely overlooked due to the technical limits of current instrumentation. With the goal of advancing PCR technology, I sought to increase the precision with which one can measure the speed of DNA denaturation.

How do you systematically study DNA denaturation?

The overall goal of the project was to see how fast DNA denatures (i.e. goes from a double to single stranded molecule) given an "insult" to the system. This insult can be anything that changes the thermodynamic stability of DNA such as: heat, pH or chemical denaturants. I wanted to develop a method to record how fast DNA responds to changes in solution conditions. In a theoretical system, the insult would be instantaneous, however, experimentally this is difficult to achieve. To this end, I tried numerous methods of measurement, a subset of which are depicted below.

I discovered that the most reproducible and systematic method was to use a stopped-flow instrument. This instrument mixes two solutions at different temperatures together. When the two lines are mixed, the solution temperature "jumps." The reaction is then observed in the downstream cuvette. An overview of the stopped-flow instrument is shown below. 

With the use of a stopped-flow instrument, precisely controlled temperature jumps can be performed. The difference in temperatures between the lines determines the resultant temperature jump. Varying the temperature of the input line can produce temperature jumps of vastly different magnitudes. 

I am interested in studying the kinetic rate conversion of fully duplexed (double stranded) to single stranded DNA. What should the temperature be of each input line and the mixed solution? The melting temperature, or Tm, of DNA is the temperature at which there is a 50% concentration of duplexed DNA in solution. The temperature of the DNA solution needs to "jump" over the Tm.

The figure below depicts the derivative melting curve, where the peak corresponds to the Tm, showing the temperature jumps performed for a particular PCR product. The input line containing the DNA is kept below the Tm. The temperature of the second line is varied to produce temperature jumps. The equilibrium temperatures (i.e. the result of the mixture of the hot and cold input lines) are shown to the right of the arrows.

PROBLEM 1: Temperature Control

The above figure underscores the need for precise temeprature control. The major challenge was overcoming the shortcomings of the instrument's temperature monitoring. The factory system is diagramed below. A thermocouple is embedded into an assembly and placed against the face of the cuvette.

My major breakthrough was the realization that a thermocouple could be threaded through the instrument to measure fluid temperature. 

At low temperatures, the divergence between real fluid temperature and reported temperature was negligible. As the temperature of the cuvette increased, toward more realistic PCR reaction conditions, the divergence was greater than 5 °C. The experiments required temperature accuracy of tenths of degrees Celsius, making this 5 degree difference unacceptable.

PROBLEM 2: DNA duplex indicator dyes are temperature dependent

When using a DNA indicator dye, the intensity of fluorescence in the solution is dependent on 1) concentration of duplex DNA and 2) the temperature of the solution. The following GIF shows the affect of a stopped-flow temeprature jump.

The loss of fluorescence could be the result of a temperature change within the cuvette (false-positive result), or denaturation (positive result).

In stopped-flow temperature-jump experiments, a major optimization step is ensuring that the cuvette temperature is the same temperature as the incoming fluid. Any difference in temperature hinders one's ability to attribute the fluorescence change to DNA denaturation. As a result, I sought to understand how one can accurately monitor temperature without direct access to the solution.

SOLUTION:  Temperature indicator dye

 The fluorescent dye Sulforhodamine B was used to accurately measure solution temperature as a function of its fluorescence. Before each experiment, the indicator dye's florescence emission was calibrated as a function of cuvette solution temperature. This involved partially dissembling the instrument and placing a thermocouple directly in the cuvette. As the temperature of the cuvette was increased, the emission fluorescence decreases. 

After calibration, the thermocouple is removed and the instrument re-assembled. The sulforhodamine B emission can be used to accurately measure temperature using first-order rate equations. Using an indicator dye, the instrument can be used in a standard operating configuration while the internal fluid temperature can be externally monitored. 

The stopped-flow instrument in the two configurations illustrated above are shown below.  Temperature calibration (right) and kinetic study (left). 

PROBLEM: Optics and data collection

To accomplish my goals, this system needs to be able to excite and record two dyes. One dye measures the DNA duplex concentration (intercalating dye) and a second indicates the temperature of the system. Once the indicator dye is calibrated, the optical system must not be moved. Any subtle variation will drastically reduce the accuracy of the fluorescent temperature measurements. The system also needs to be able to provide real-time scaled temperature information from the Sulforhodamine B dye fluorescence. The factory supplied software/hardware cannot accommodate these parameters. Two separate systems (optical and stopped-flow) need to be used in conjunction to study denaturation. My custom system records the fluorescence in LabVIEW and a second factory-standard system controls and regulates the instrument. 

SOLUTION 1: OPTICAL HARDWARE

The stopped-flow cuvette assembly determined the optical instrumentation. The assembly is essentially an aluminum cage with four ports that heats and cools the cuvette (above). Two sides of the cuvette are utilized by the regulation thermocouple and peltier. This leaves two ports to place the excitation and emission optics. To get two independent emission intensities out of one cuvette face, the emission light is split using a dichroic mirror into two photomultiplier tubes (PMT), one for each channel (DNA and temperature indicator dye). 

The excitation sources for each dye are combined using a second dichroic mirror and focuessed into a fiber bundle. 

SOLUTION 2: Synchronization of Instruments and data collection

Data recording needs to be synchronized to the start of the reaction. The reaction starts when each syringe is pushed and mixed together. The instrument outputs a 5V TTL signal that corresponds to the syringe's movement. The LabVIEW program waits for this signal and records one fluoresence channel at 1MHz. 

Data Analysis

Ultimately, I would like to find the half-life of denaturation as a function of solution temperature. This relation can be utilized in PCR optimization to find the minimum denaturation temperature (related to the Tm) and melting time needed to achieve efficient amplification. The assumption that we started with (and later proved) was that DNA denatures as a first-order reaction. As the temperature increases past the melting temperature, the denaturation rate increases. The two following figures show the temperature jumps related to the melting temperature and the resulting denaturation curves. 

The following figure shows the denaturation curves for each of the temperature jumps.

From the assumption of a first-order reaction we can extract the rate constants from the denaturation plots. The equation for a first-order reaction is:

This equation gives the concentration of reactant as a function of time and the rate constant, k. The rate constant can be used to find the half life (t1/2):

Two methods were used to find the rate constant (logarithmic and least-squares). The lower left figure shows the logarithmic method. The data is plotted log-linearly and the slope of the linear region was found. The least-squares method is shown on the lower right, a Scipy module (curve_fit) was used to extract parameters from an inputted model equation.

Once the DNA denatures, the fluorescence plateaus. One challenge was algorithmically extracting rate constants from the exponential portion of the data and ignoring the plateau region. To find the region of interest, the data was sub-sampled with increasing windows. For each of the windows, rate constants were found and a curve fit to the data. The residual was found for each of the sub-sampled windows. The model with the smallest residual was chosen. The graphs below illustrate the windows and corresponding curves. 

The logarithmic and least squares fits are shown below with the filtered original data.