Sunday, March 10, 2013

Catch a colloid by the tail !

About five years ago, an interesting twist [1] on the resistive pulse technique emerged from the Dekker lab at TU Delft (Netherlands). Their set up is shown in the sketch on the left. One end of the DNA was attached to a polystyrene bead which is held in place by a spot of laser light: a very useful innovation in nanotechnology known as a Laser Optical Trap (LOT) (aka Optical Tweezers). When a voltage is applied and the DNA starts to translocate, the LOT holds it back and "frustrates" the translocation. As the DNA pulls at its tether, the bead is displaced slightly from its equilibrium position which gives a way to directly measure the force acting on the DNA. Instead of yielding the translocation time this method yields the "tether force" together with the conductance change of the pore. This set up can be used to test the idea of the "hydrodynamic origin" of the resistive force discussed in my last Blog. I was able to calculate [2] the tether force using a modification of the theory for translocation times discussed earlier, and this simple analytical formula could be compared with the tether force measurements [3].

This is shown in the panel to the left. The top sub figure shows that the tether force is proportional to the applied voltage. The force per unit applied voltage is plotted in the lower figure against the pore radius (R). The data shows quite clearly the 1/ln R dependence of the force predicted by theory. The dashed curve is obtained if the DNA "bare charge" is used. The solid curve is obtained if the DNA "effective charge" is considered less than the bare charge by a fixed ratio q, considered here as a fitting parameter.

The figure on the right shows a more recent [4] experimental test of the hydrodynamic theory emerging out of the Keyser Lab at the Cavendish.  The Keyser lab has capitalized on an astoundingly simple (= cheap!) way of producing nanopores. They heat a glass microcapillary with a laser and use the traditional glass pulling technique to obtain a sharp tip. Internal diameters of 10-100 nanometers can be obtained in this way. The experiment shows the force signal as a trapped DNA is gradually pulled out of the pore. The force can be calculated using the lubrication theory [5,6] for electrokinetics and is shown by the red dots in the lower panel.

These experiments give us confidence that the principal resistive force in DNA translocation does indeed arise primarily from hydrodynamic drag in the pore region. The challenge now is to use this knowledge to evolve new tools for characterizing DNA such as the base sequence, interactions with proteins and fundamental questions related to the behavior of DNA as a charged polymer. This is still an open book with many exciting possibilities in basic science as well as in nascent technologies. Already, a new term is being used in this context "DNA Force Spectroscopy"!

Acknowledgement:  My research in this area has been supported by the NIH (USA) and by the Leverhulme Trust (UK).


[1] Optical tweezers for force measurements on DNA in nanopores (2006) UF Keyser, J van der Does, C Dekker & NH Dekker Rev. Sci. Instruments 77 (10)

[2] Electrokinetic-flow-induced viscous drag on a tethered DNA inside a nanopore (2007) S Ghosal Physical Review E 76 (6), 061916

[3] Origin of the electrophoretic force on DNA in solid-state nanopores (2009) S van Dorp, UF Keyser, NH Dekker, C Dekker & SG Lemay Nature Physics 5, 347 - 351

[4] Single macromolecules under tension and in confinement  (PhD thesis, Cambridge University) Oliver Otto 2011

[5] Lubrication theory for electro-osmotic flow in a microfluidic channel of slowly varying cross-section and wall charge (2002) S Ghosal Journal of Fluid Mechanics 459, 103-128

[6] Electrophoresis of a polyelectrolyte through a nanopore (2006) S Ghosal Physical Review E 74 (4), 041901
[7] Effect of salt concentration on the electrophoretic speed of a polyelectrolyte through a nanopore (2007) S Ghosal Physical review letters 98 (23), 238104

Saturday, March 9, 2013

How fast do DNA zip through nanopores?

The resistive pulse technique provides two basic observables from which to infer the properties of the translocating molecule. These are (a) the blockade time (b) the relative conductance change.  The first of these is a measure of the speed (v) of the translocating molecule.

The force driving the translocation is the electrical force acting on the part of the DNA inside the pore. This force is the voltage drop across the membrane times the charge on the polymer within the pore. For typical parameters, this amounts to about 20 pico Newton (pN). Since inertia plays no role at such small scales, to calculate the speed we need to set this driving force to equal a resistive force that will depend on the speed of translocation (v). What is the origin of this resistive force? I made the hypothesis that the resistive force arises primarily from the hydrodynamic drag on the part of the polymer that occupies the pore. The frictional drag from the polymer coil outside the pore as well as the "entropic force" required to straighten the polymer against thermal fluctuations are both small compared to this hydrodynamic drag from the pore. If the primary drag force arose from within the pore, the speed v would be independent of polymer length. This appears to hold to a good approximation from the experimental data.

The hydrodynamic drag on a rod (the DNA) translating through a slightly larger pore (of arbitrary cylindrically symmetric shape) may be calculated using the classical "lubrication theory" of fluid mechanics. In our problem there is some additional physics not encountered in the classical problem and it is this: both the DNA and the wall of the capillary are charged and there is an applied electric field. As explained by Peter Debye all charged macromolecules carry a cloud of mobile counter-ions (positive ions or cations in the case of DNA) that "shield" their electrical interactions with other objects. The electric field acts on these counter-ions to create a body force that drives a jet of fluid upwards through the gap as the DNA moves downwards. This "electroosmotic" effect must be included in the calculation of the drag. Nevertheless, even with this additional effect the problem can be solved and an expression for the velocity obtained in closed form. The graph to the left shows how this formula measures up against the experimental data. The interesting thing about this graph is that it does not involved any "adjustable" parameters even though reasonable approximations (detailed in the papers cited below) need to be made. The upper dashed curve is calculated using the DNA bare charge and the lower curve uses the DNA "effective" charge in accordance with the Manning theory of counter-ion condensation.


1. Electrophoresis of a polyelectrolyte through a nanopore S Ghosal (2006) Physical Review E 74 (4), 041901

2. Effect of salt concentration on the electrophoretic speed of a polyelectrolyte through a nanopore (2007) S.Ghosal Physical review letters 98 (23), 238104

Friday, March 8, 2013

(Background) How polymers cross membranes

A cell is enclosed in a lipid bi-layer membrane which serves as a reaction chamber for the biochemical processes of life. Within the cell there are various organelles such as the nucleus, mitochondria and so on which too are surrounded by membranes. In order for the cell to function, some but not all bio-molecules must be able to cross the membrane. This usually happens through proteins that form pores on these membranes. These pores are very small, often a nanometer or so in  size. They serve as border "check points" for the intra-cellular and intra-organelle "traffic".  Many important bio-molecules are long chain polymers e.g. DNA, RNA and proteins. The physical process by which such polymers cross membranes is of importance for understanding how cells function.

As in other areas of science, real insight is often gained by studying an effect in isolation free of the influences of non-essential phenomena. Biologists call this "in vitro" experiments (in vitro = in the test tube as opposed to inside a living organism or "in vivo"). In 1996, Kasianowicz et al. published a very beautiful in vitro experiment that mimicked the natural process of polymer translocation across membranes. A version of the experiment (figure taken from the later paper by Meller et al.) is shown in the left. A natural protein that goes by the name of "alpha-hemolysin" was extracted from the "staph" bacteria Staphylococcus aureus. This protein is a heptamer - it comes in seven parts like Leggo pieces. When the pieces are absorbed on to a lipid membrane, they self assemble forming a pore. In the experimental set-up the lipid membrane formed the partition between two baths containing salt water across which an electric voltage was applied. The assembly of the pore was signaled by the current that would start to flow as soon as a conducting path through the membrane was established. When a small amount of DNA was added to the negative side of the bath, every now and then, the electric field would shoot a DNA molecule through the pore (DNA being negatively charged). Each time this happened, the pore would be transiently blocked creating a dip in the current signal. The current is "quantized" that is, it only takes one of two values the low one when the DNA is in the pore and the high one when it is out. The signal contains information about the length of the DNA strand, the density of DNA in the cell and perhaps even the identity of the bases of the DNA.

This pioneering paper has led to a flood of experimental work refining the technique which has come to be known as "the resistive pulse technique". The idea that the method can be refined to directly read the base sequence of DNA has led to a nanotechnology gold rush for the "Thousand Dollar Genome", the goal of sequencing a person's DNA at a cost of less than a thousand dollars (the Human Genome Project cost 3 billion dollars). Perhaps on a less grand scale, it raises some interesting physics questions such as how fast does the DNA go through? Can this speed be controlled and so on. I will be posting on these issues in future blogs .... so don't go away!