Tracking the Brownian motion of DNA-functionalized magnetic nanoparticles for conformation analysis beyond the optical resolution limit

Abstract

Brownian motion provides access to hydrodynamic properties of nanoscale objects independent of their optical resolvability. Here, we present a diffusion-based approach to infer effective particle size distributions of DNA-functionalized magnetic nanoparticles (MNPs), consisting of a magnetic core and a polystyrene shell, in a regime where direct geometric sizing is limited by optical diffraction. Using multi-particle tracking microscopy, we analyze the Brownian dynamics of MNPs grafted with double-stranded DNA (dsDNA) of varying contour length under low-salt conditions. A physically motivated model is introduced that relates dsDNA contour length to an effective hydrodynamic diameter via an attenuated corona description. The measured diffusion coefficient distributions exhibit a systematic and monotonic dependence on dsDNA length in quantitative agreement with the model. While the tracked objects are predominantly dsDNA-mediated agglomerates rather than isolated nanoparticles, clustering does not obscure the length-dependent signal. Instead, the dsDNA corona determines the hydrodynamic scaling, whereas agglomeration mainly introduces an offset and distribution broadening. These results demonstrate that Brownian dynamics enables robust readout of biomolecular length scales even far below the optical resolution limit. The distribution-based approach is inherently tolerant to polydispersity and aggregation, making diffusion-based tracking a simple and promising strategy for future biotechnological and biomedical assays.

Figures (10)

• Figure 1: Surface-functionalization of MNPs with dsDNA strands results either in a brushed or coiled conformation, depending on the DNA length and grafting density. Observation of the particle's Brownian motion via optical microscopy was used to distinguish between these states.
• Figure 2: Sketch of the experiment and data evaluation. (a) An optical bright-field microscope equipped with a high-resolution camera was used to record the motion of dsDNA-functionalized MNPs that were free-floating in a container cell. (b) A particle tracking algorithm provides 2D trajectories for each MNP visible in the field of view (FOV). (c) The mean squared displacement (MSD) was calculated for each particle trajectory and plotted as a function of lag time $\tau$, denoting different time frames for trajectory analysis. (d) The obtained MSD is closely connected to the size distribution of observed MNPs, which was examined via transmission electron microscope (TEM) images. (e) Histogram for the measured MNP diameters obtained from TEM images, fitted by a log-normal distribution function. A mean particle diameter of $165\pm6~\mathrm{nm}$ was obtained.
• Figure 3: Predicted effective diameter distributions $f_{d,\mathrm{model}}\left(d\right)$ for dsDNA-functionalized MNPs using the attenuated hedgehog model with $\gamma = 0.6$. The gray band denotes the Abbe-diffraction-limited regime for the given numerical aperture and wavelength range. Within the black band, (dsDNA)-MNPs fall below the Abbe limit.
• Figure 4: Model diffusion coefficient distributions $f_{D,\mathrm{model}}\left(D\right)$ derived from the effective diameter distributions in Figure \ref{['fig:d_model']} via the Stokes–Einstein relation. Longer dsDNA systematically shifts the distributions to lower D.
• Figure 5: Experimental diffusion coefficient distributions $f_{D,\mathrm{exp}}(D)$ obtained from optical tracking for bare MNPs and MNPs functionalized with 340, 500, 720, and 2000 dsDNA. Lognormal fits (lines) provide the basis for inverse reconstruction of effective diameters shown in Figure \ref{['fig:d_exp']}.