Diffusion correction and concentration measurement

The relative abundance of each DNA fragment in the dsDNA ladder was calculated from the area of each Gaussian peak in the kernel density estimate (KDE) plot, , where a is the area, A is the maximum height at centroid and σ is the standard deviation of the fitted Gaussian. The contrast magnitude achievable with the 100 bp species approached the limit where the instrumental readout in terms of counting molecules is quantitative.

To account for differences in binding rates and thus molecule counts caused by varying diffusion speeds, we applied a correction to the measured mass distributions (16). We assumed that the binding rate constant scales with the diffusion coefficient, which has been reported to be roughly proportional to (base pair)^−0.72 for DNA (i.e., , where k_i is the binding rate constant for DNA component i and α is a scaling factor) (21). We assumed that the scaling factor α is constant for all DNA components. To estimate the scaling factor α, an exponential function was fitted to the number of landing events vs time resulting in an average binding rate, k. The scaling factor was calculated as: , where <bp> is the average number of base pairs of all the DNA components in solution calculated based on the distribution of each DNA component, , where bp_i is the number of base pairs and a_i the relative abundance measured experimentally of DNA component i, and N is the total number of species in solution. To accurately estimate the proportion of each DNA fragment in solution, it is important to account for landing events that occur between the time when the sample is added (t_addition) and when data acquisition starts (t₀). We accounted for this by fitting the exponential decay of measured binding events (from t_addition) from the addition of sample to completion of all sample binding (t = infinity) (Supplementary Figure S2). Experimentally, we integrated from a given time t₀ = 15 s after addition of sample up to a later time, t_final = 135 s, when the acquired movie ended. Relating these two, the corrected intensity was given by: , where a’_i is the intensity of DNA component i corrected over all time, and a_i is the experimentally measured abundance. The corrected mass distribution was then renormalized.