DNA: A Biological Spring

Motivation. Over the past 20 years, the development of sensitive physical techniques such as atomic force microscopy (AFM) (http://www.nanoscience.com/education/afm.html) and optical tweezers (http://www.stanford.edu/group/blocklab/Optical%20Tweezers%20Introduction.htm) have allowed us to characterize the mechanical properties of DNA molecules in great detail. Both of these techniques rely on isolating a single molecule of DNA and then probing it with physical force to see how the molecule responds to being poked and prodded. By studying how DNA stretches and twists at the single-molecule level, we have uncovered important details about how processes such as DNA replication and transcription occur. In this problem, you will explore how one of these techniques – optical tweezers – has allowed us to calculate the tension in DNA.

Question 1: Experimenters in the field of single-molecule biophysics will tell you that it is tedious work to isolate single molecules of DNA for studies of this sort. Why might it be worth the effort? Can you think of a reason why we might want to study DNA (or any biological molecule, for that matter) one molecule at a time, rather than as an ensemble of millions of molecules in a test tube?

Experimental Set-up. If someone asked you to measure the spring constant k for a DNA molecule, how might you do so? Well, as with any spring, you’d probably like to be able to pick it up and tug on it, to see how much force you must apply in order to stretch it a certain distance. This would give you a sense of how taut or tense the spring is, and therefore a sense of its spring constant. Unfortunately, a single DNA molecule is tiny, so we can’t just go to the bathroom cabinet and get a pair of everyday tweezers to pick it up. We must devise a more clever tweezer!

The diagram below presents the key features of one such clever device, the “optical tweezer.” Later in the course we may have the chance to discuss this set-up in more detail, but for now don’t worry too much about how it works. The important thing to know right now is that one end of the DNA molecule is chemically attached to a small polystyrene bead (the bead’s radius is about 10^-6m), which is “trapped” in space by one or more laser beams. (If the bead were not trapped, it would just float haphazardly around the fluid in which the experiment takes place, making it almost impossible to study.) The other end of the DNA molecule is fixed in place, such as by attaching it to a surface, as shown in the figure.

Figure 1. DNA Manipulation Experiment Using Optical Tweezers.

Since the bead is trapped in the center of the laser beam (called the beam’s “focus”), it moves as the focus moves. Why the bead moves with the focus of the beam is not at all obvious… stay tuned for a discussion later in the course! If you move the laser focus to the right, the bead goes with it. By moving the focus of the beam ever so slightly, we can begin to stretch the DNA. Moving the focus of the beam just a few nanometers to the right causes the DNA to be stretched by a measurable force, and we can begin to construct a plot of the bead’s position as a function of the applied force.

Estimating the dsDNA spring constant. When optical tweezer experiments are performed on double-stranded DNA (dsDNA), data of the following form are obtained (the horizontal axis is labeled in micrometers, 10^-6 m, and the vertical axis in picoNewtons, 10^-12 N). “Extension” refers to the length beyond the length DNA would have if it were relaxed, i.e., if it were not being stretched by the optical tweezer.

Figure 2. Stretching dsDNA. The “B-form” dsDNA is the type that most often exists under normal physiological conditions in the cell.

To see a video of the optical tweezer experiment that produced this data, click on one of the following links (remember that the DNA is always invisible in these videos, because it’s small!): http://www.youtube.com/watch?v=fZDQ1s79Mpc or http://alice.berkeley.edu/~steve/DNAmovie.mpg

As you can see from the data, the DNA behaves somewhat differently depending on how much force is applied. Let’s try to examine that behavior a little more closely.

Question 2: How might you explain the observed behavior in each of these regions? What might the DNA look like and how might it be deformed in each region? In particular, describe what you think is happening in each of the following portions of the data: (a) when the applied force is less than a few pN, (b) when the applied force is between a few and 65 pN (“B-form region”), and (c) when the force applied is greater than 65 pN (“over-stretched region”).

Clearly, DNA is not an ideal spring obeying Hooke’s Law – it is more complicated than that. A model that more accurately describes the behavior of dsDNA as a whole must itself be much more complicated (for example: http://en.wikipedia.org/wiki/Worm-like_chain). Nevertheless, there is still a great deal we can learn from the simple model of an ideal spring.

Question 3: We can model the dsDNA as an ideal spring over certain ranges of extension, although over the whole range clearly the ideal spring model is inadequate. What is the approximate spring constant for B-form dsDNA, the form of dsDNA most commonly found under normal physiological conditions? Do you think it is reasonable to treat dsDNA as a simple spring when it is not in the B-form state? Why or why not?

Question 4: Optical tweezers don’t exist inside living cells! What then might create the tension on DNA in a real living system?

Question 5: In this problem we have seen that DNA can be stretched in a spring-like manner to adopt different structures and different lengths. Why is it biologically necessary that a molecule of DNA be able to assume such a diverse range of structures? Can you think of situations where it is beneficial that a molecule of DNA be coiled tightly, and a situation where it is beneficial that it be stretched out?