Determining Trap Compliances, Microsphere Size Variations, and Response Linearities in Single DNA Molecule Elasticity Measurements with Optical Tweezers

We previously introduced the use of DNA molecules for calibration of biophysical force and displacement measurements with optical tweezers. Force and length scale factors can be determined from measurements of DNA stretching. Trap compliance can be determined by fitting the data to a nonlinear DNA elasticity model, however, noise/drift/offsets in the measurement can affect the reliability of this determination. Here we demonstrate a more robust method that uses a linear approximation for DNA elasticity applied to high force range (25–45 pN) data. We show that this method can be used to assess how small variations in microsphere sizes affect DNA length measurements and demonstrate methods for correcting for these errors. We further show that these measurements can be used to check assumed linearities of system responses. Finally, we demonstrate methods combining microsphere imaging and DNA stretching to check the compliance and positioning of individual traps.


Determining force and displacement scale factors
The force scale factor α is determined by measuring the DNA overstretch transition. As described in detail in Ref. 22, we measure the PSD voltage at which this occurs by finding the midpoint (which corresponds to F=64 pN) between the intersection points of a linear fit to the overstretch plateau and two polynomial fits to the sections of data before and after the overstretch transition plateau. The displacement scale factor β is determined as described in detail in Ref. 22. In brief, the values of that correspond to the value = 33.4 pN, where = , were determined for the two different DNA construct lengths ( 1 and 2 ). At this force Eq. (6) gives = ( 2 − 1 ) ( 2 − 1 ) ⁄ , where 1 and 2 are the known contour lengths of the two DNA constructs.

DNA Force-Extension Measurements
Multiple force-extension curves for the two different DNA construct lengths were collected. Tethers were formed by briefly bringing the trapped DNA-and anti-dig-coated microspheres together and then separating them while checking for the increase in PSD signal indicative of increasing force on the microspheres. Once a DNA tether was formed, a force-extension curve was measured by increasing at a fixed rate of 500 nm/s between values 1 and 2 , where 1 is the largest control voltage such that the PSD signal does not differ from background, and 2 corresponds to a microsphere separation distance large enough that the DNA tether will either detach or complete an overstretch transition. PSD data were recorded at a rate of 1 kHz. The background PSD signal as a function of was also subtracted from each force-extension dataset.

Error in the determination of the series trap compliance
We analyzed uncertainties/error sources in the determination of the compliance parameter  by considering the effect of various factors on the use of Equation (4)  iii) Uncertainty in the force measurements is caused by an uncertainty of 2% in the force calibration factor α, due to uncertainty in the DNA overstretch transition force plateau reported by Wenner et al. (Ref. 35) and random measurement errors in our overstretch transition measurements (as discussed by delToro et al. (Ref. 22)). Through Eq. (4) this uncertainty results in an uncertainty of 1.5% in the determination of . iv) Uncertainty in the trap displacements is caused by an uncertainty of ~0.7% in calibration factor  as discussed by delToro et al. (Ref. 22). Through Eq. (4) this uncertainty results in an uncertainty of 0.95% in the determination of . v) Analysis of Equations (1), (2), and (4) indicate that the approximation that the DNA force-extension relationship is linear in the range from 25-45 pN, when it actually has a small nonlinearity, causes an error of 0.96% in the determination of .
Note: The five sources of uncertainty listed above do not have completely independent effects. By systematically varying all these parameters together, we calculated that the maximum induced uncertainty in gamma is ~6%.
vi) Finally, we considered the effect of noise in the force measurements, due to Brownian and instrumental noise. We investigated this by generating an ensemble of simulated datasets with the DNA force-extension law fixed according to Eq. (1) but with random Gaussian noise added to each dataset. The force noise level in these simulated datasets was set equal to that in the measured datasets. By fitting these simulated datasets to Eq. (4) we determined that this noise causes 0.3% uncertainty in the determination of .