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DNA Replication Rate by Phi29 Polymerase
Jared Matzke and Michael Joseph
Advisor: Greg Pawloski
Attempts were made to determine the rate that a specific type of viral DNA is replicated by the enzyme \x{03a6}29 Polymerase. This was done by stretching the DNA under a microscope and observing the change in the extended length as the replication reaction occured. Numerous mechanical and biochemical issues prevented successful measurements and calculations of the rate. A backup measurement of the brownian motion of microbeads in the buffer fluid confirmed the assumtion that the fluid had the same viscosity as water.
DNA is a biological polymer that is generally made up of two strands connected by nitrogen containing base pairs located along each strand. The enzyme polymerase playes a key role in the replication of DNA molecules by traveling along the strands and separating them while adding the corresponding nitrogenous base pairs to both separated strands, leaving behind two daughter DNA molecules that are identical to the original. However, if the polymerase is attached specifically to one strand of the double stranded DNA, it can be used to separate the two strands while only replicating the strand it was attached to. If the polymerase and DNA proceed through the replication reaction in this way, the rate that the polymerase travels along DNA can be determined by finding the rate that the double-stranded DNA becomes single stranded.
Double- and single-stranded DNA are mathematically described by the Worm-Like Chain model of polymers. Using this model, the force required to stretch the DNA can be written as a function of various known properties of the DNA and its total extension \x{0394}R, as shown in the equation below.
L and Lp are polymer properties known as the characteristic length and persistance length of the polymer. Because these values are different for single- and double-stranded DNA, a constant tension force will produce a different extended length between single- and double-stranded DNA. So by applying a constant stretching force to a double-stranded DNA molecule, and observing the rate of change in extended length as the polymerase splits it into a single strand, the rate that the polymerase moves along the DNA can be determined.
A double-stranded DNA molecule will be modified so that one strand will bind to a stationary surface on one end and a microbead on the other. The opposite strand will be modified to give a priming location for a polymerase to attach. A horizontal fluid drag force will be applied to the microbead to stretch the DNA and a vertical magnetic force will be used to hold the bead up off the stationary surface. The horizontal drag force on the bead can be described using Stoke's relation as shown below.
Here, R is the bead radius, \x{03b7} is the fluid viscosity and v is the horizontal velocity of the fluid. In a horizonal, rectangular channel, this velocity profile is given as
where Q is the fluid volume flowrate, h and w are the height and width of the channel and z is the height off the bottom surface of the channel. Since a microscope could only be used to find the horizontal position and not the vertical position, force balance between the horizontal componant of the tension force and this horizontal drag force can be solved to find the vertical position of the bead z. This value can then be used to determine the vertical componant of the tension force, which must be equal and opposite to the magnetic force. Once all forces on the bead are found, the extended length of the DNA, \x{0394}R, can be calculated.
The polymerase can then be attached to the DNA to begin the replication reaction. As the DNA splits, the tension force holding the bead will increase, causing the bead to move backward, against the flow of the fluid. The rate that the bead moves is then proportional to the rate that the polymerase moves along the DNA.
The apparatus is shown in the figure below.
A mechanical syring pump is used to pull fluid through a flow cell situated beneath a microscope. An air spring is used to create a pressure damper that will reduce any mechanical vibrations of the pump before they reach the flow cell. The microscope can record the horizontal position of beads in the fluid as it flows throug the cell and the magnet provides a constant vertical magnetic force over the microscope field of view.
The flow cell is comprised of a piece of double sided tape sandwiched between two glass slides. The tape has a narrow channel cut through the middle to allow fluid flow. The bottom glass slide has been coated in a protien to allow the DNA strands to attach, and the upper glass slide has been drilled to allow the attachment of tubing that will carry fluid to and from the cell.
Due to numerous bio-chemical and mechanical issues, beads that had been teathered to the slide by an attached strand of DNA were not found. Possible reasons include improper modification of the DNA. If the modification process had not worked, the biological molecules required to bind the DNA to the slide or the bead may not have been present, which would cause the attachment process to produce no results. However, since the DNA was not visible using the standard light microscope, and an electron microscope would have destroyed it, visibly determining what aspect of the modification process had failled was not possible. Other issues included; pressure leaks through to holes in the epoxy seals between the tubes and slides, the cost of the protein coated slides preventing the use of any chemical methods that may damage their functionality, transportation and temperature changes of these slides that possibly degrade the proteins, or the flow speed being too high to allow for DNA and bead attachment.
A backup measurement was used to confirm the assumption that the fluid used through the flow cell would have the same drag properties as water. The fluid consisted of water with very small concentrations of magnesium chloride, saline and various protiens and chemicals necessary for DNA and polymerase to function. These additions may have altered the viscosity of the water, causing a deviation in the fluid drag force. By adding a small concentration of the microbeads to a transparent dish containing this buffer fluid, their random motion due to collisions with the fluid molecules can be observed.
The brownian motion model of this movement relates the mean squared displacement of the beads to the fluid viscosity and the time elapsed, as shown below.
where a is the radius of the bead, T is the fluid temperature and t is the time in seconds. By graphing the left half of this equation versus the time, a linear plot should emerge. The slope of this plot can then be used to determine the fluid viscosity.
The fluid viscosity was determined to be (8.80±0.34)•10^(-3) Pascal seconds. This is less than one sigma away from the expected value of 9.07•10^(-3) Pascal second. This confirmed the assumption that the buffer solution could be approximated as water.
Although the rate of DNA replication was not determined, numerous chemical and mechanical issues were recognized, analyzed and resolved. This analysis can be used to generate a better method for the completion of this expirement. The assumption that the buffer solution would behave like water when applying a viscous drag force to the microbead was confirmed.
N. A. Tanner, A. M. van Oijen, “Visualizing DNA replication at the single- molecule level,” Methods Enzymol. 75, 259–278 (2010).
Kelly Williams, Brendan Grafe, “A single molecule DNA flow stretching microscope for undergraduates,” American Journal of Physics. 79, 1112 (2011).
Alberts, et al. Molecular Biology of the Cell, 4th Edition. Garland Science, New York, 2002
Brown, Andrew, and Philip Johnson. "Wormlike chains." Biocurious: Wormlike Chains. N.p., 2013. Web. Mar. 2014.
Khalid, Asma, and Muhammad S. Anwar. Tracking Brownian Motion through Video Microscopy. Tech. LUMS School of Science and Engineering, 23 Aug. 2010. Web. 11 Apr. 2014.
Bergman, T. L., and Frank P. Incropera. "Thermophysical Properties of Matter." Fundamentals of Heat and Mass Transfer. Hoboken, NJ: Wiley, 2011. 1003. Print.
Thanks to Greg Pawloski and Kurt Wick for their help and ideas on how to solve our DNA problems. Thanks also to Gordon Stecklein for helping us get into our lab room when our door was broken.
-- Main.josep296 - 15 May 2014d