Single-molecule dissection of stacking forces in DNA
Authors: Kilchherr Fabian , Wachauf Christian , Pelz Benjamin , Rief Matthias , Zacharias Martin , Dietz Hendrik 
Published: September 2016

INTRODUCTION
In DNA double helices, hydrogen bonds connect the base pairs across the two strands, and stacking bonds act along the helical axis between neighboring base pairs. Our understanding of DNA and the way it is processed in biology would profit from improved knowledge about the elementary bonds in DNA. Detailed knowledge of the time scales for breaking and forming individual base pairs and base-pair stacks would also help to make more informed decisions in the design of dynamic DNA-based nanoscale devices.

RATIONALE
The goal of this work is to measure the dynamics of DNA base-pair stacking at the level of individual base-pair steps. Because stacking interactions act perpendicularly to the hydrogen bonds, it should be possible to use mechanical forces to break stacking while leaving hydrogen bonds intact. To realize such measurements, we combine the positioning capabilities of DNA origami with single-molecule manipulation, as enabled by dual-beam optical traps. To make the weak single–base-pair stacking interactions experimentally accessible, we prepared parallel arrays of blunt-end DNA double helices to take advantage of avidity effects when these arrays form stacking interactions (see the figure). Our design allowed controlling the number and the sequences of the base-pair stacks. Noise-suppressing by stiff DNA origami beams connected by a flexible polymer tether enabled the repeated detection of unbinding and rebinding of stacking contacts at low forces (down to 2 piconewtons) with high time resolution (up to 1 kHz).

RESULTS

We sampled all 16 sequence combinations of installing a particular interfacial base pair on the array on the left beam and another base pair in the array on the right beam, and we created arrays with two, four, and six blunt ends. We could measure the force-dependent lifetimes for all base-pair step sequence combinations in the presence of 20 mM MgCl
2
, which is a condition typically used in DNA nanotechnology. For a subset of base-pair step combinations, we also obtained data in the presence of 500 mM NaCl, which mimics the conditions in the cell nucleus. The base-pair stack arrays spontaneously dissociated at average rates ranging from 0.02 to 500 per second, where the dissociation time scale strongly depended on the sequence combination and the stack array size. For a given sequence combination, larger array sizes always had larger lifetimes, as expected from avidity. Another key feature revealed in the lifetime data was the low sensitivity of the stacking interactions on the extent of pulling force. This phenomenon reflects short-ranged interaction potentials. Concerning rebinding of the stack arrays, we found that the rebinding kinetics depended much more strongly on the applied force, which may be understood by considering that rebinding of the stacks requires a thermally activated contraction of the flexible tether—which was the same for all variants—against an opposing force tether contraction. However, the rebinding kinetics was independent, within experimental error, of the base-pair step sequence combination and the size of the array under study. We used a model to estimate the free-energy increments per single base-pair stack from the kinetic rates that we measured with stack arrays. The free-energy increments per stack ranged from –0.8 to –3.4 kilocalories per mole. Our data reveals a trend in the stacking-strength hierarchy that may be associated with the extent of geometrical atomic overlap between the bases within a base-pair step.

CONCLUSION
Our data provides a quantitative basis for the rational design of dynamic DNA-based nanoscale machines and assemblies. Nanoengineers can directly read off the expected lifetimes of stack arrays for all sequence combinations and for various array sizes and at salt conditions that are commonly used in the field. With this data, design solutions for transition kinetics may be generated that cover several orders of magnitudes in lifetime, from milliseconds to several seconds. The sequence-resolved information obtained in our experiments may inform kinetic models of DNA hybridization and may help in adjusting force fields to perform more realistic molecular dynamics simulations. More generally, our experimental methods advance the capabilities of single-molecule mechanical experiments. Using the tethered-beam system, target molecules may be placed and exposed in controlled orientations and stoichiometry so as to study the weak forces occurring between them in solution. A variety of interactions between various kinds of molecules may be studied in the future due to the modularity and the addressability of the DNA origami–based tethered-beam system.

How strong is DNA base-pair stacking?
Schematic illustration of the experimental system that we developed to measure the strength of base-pair stacking on the level of single particles. The system consists of two tethered DNA origami beams that feature parallel arrays of blunt-end DNA double helices. The beams may be attached to two micrometer-sized beads for manipulation in a dual-beam optical trap. With this system, we could measure lifetimes at which DNA base-pair stacks spontaneously dissociate as a function of force applied in the helical direction.