Tracking Longitudinal Rotation of Silicon Nanowires for Biointerfaces.

The rolling motion (i.e., longitudinal rotation) of nanomaterials may serve as a proxy to probe microscopic environments. Furthermore, nanoscale rotations in biological systems are common but difficult to measure. Here, we report a new tool that measures rolling motion of a nanowire with a short arm grown at one end. We present a particle detection algorithm with subpixel resolution and image segmentation with principal component analysis that enables precise and automated determination of the nanowire orientation. We show that the nanowires' rolling dynamics can be significantly affected by their surroundings and demonstrate the probes' ability to reflect different nanobio interactions. A non-cell-interacting nanowire undergoes rapid subdiffusive rotation, while a cell-interacting nanowire exhibits superdiffusive unidirectional rotation when the cell membrane actively interacts with the nanowire and slow subdiffusive rotation when it is fully encompassed by the cell. Our method can be used to yield insights into various biophysical and assembly processes.

Tracking the rotation of a microscopic particle can serve as a sensitive probe of the local environment in both biological and nonliving systems. In three-dimensional space, rolling motion (i.e., longitudinal rotation) is arguably the subtlest and the most sensitive motion, generally requiring just nanoscale forces to actuate;[1] the other five degrees of freedom in motion being translations in the x, y, z directions, rotation in-plane, and rotation out-of-plane (Figure ). In addition to the small moment of inertia associated with the rolling motion (Supporting Information S1), when compared to translations or planar rotations, rolling motion generally involves the least amount of free space, such that we are more likely to observe rolling motion in a crowded environment where other motions are constrained.

Figure 1

Overview of the rolling tracking method. (A) Schematic diagram of a kinked silicon nanowire with its projection (gray) on the detection plane (xy plane). The nanowire can translate in three directions (x, y, z) and rotate longitudinally (θ), in-plane (φ), and out-of-plane (ρ). In the experiments, translation in z-axis and rotation out-of-plane of the nanowire main segment are negligible. (B) Right: schematic diagram of the kinked silicon nanowire from the top (perspective 1 in A); left: schematic diagram of the arm (perspective 2 in A) with the arm length (l), apparent thickness (2r), and longitudinal orientation (θ) annotated in red. (C) Optical microscope images of a kinked silicon nanowire in different longitudinal orientations, Scale bar: 2 μm.

Tools to track rolling motion utilize either an optical or a structural asymmetry. In 2005, Yajima and Cross introduced a side arm (structural asymmetry) to a microtubule to experimentally observe microtubule rotation induced by kinesin.[2] Following this, Yajima et al. tracked microtubule rotation with higher precision by labeling microtubules with nanocrystals (optical asymmetry) and tracking the rotation with a three-dimensional microscopy.[3] The Yu group tracked the rolling motion of dual fluorescent labeled (optically asymmetric) Janus rods (∼500 nm in diameter) bound to endosomes to study the rotational dynamics of endosomes during intracellular transport[4] and to study how the distribution of ligands on the Janus particle surface affects the cellular internalization process.[5] In a study of rolling motion in a nonliving system, the Biswal group introduced a kink (structural asymmetry) in a chain of DNA-linked colloids (∼1 μm diameter) and studied how the no-slip boundary condition affects the rolling diffusivity.[6] While these methods yield measurements of rolling motion with high precision, their applications are limited by the probes’ significant thicknesses and complex fabrication.

Here, we introduce a new method for tracking the rolling motion of a nanoscale L-shaped particle that is both structurally and optically robust, easy to synthesize, and synthetically tunable. Specifically, we track the rolling motion of a kinked nanowire by measuring the projected lengths of the nanowire arm on the microscope detection plane (Figure ). While reminiscent of the bent microtubule, silicon nanowires provide better structural stability and tunable rigidity (Figure S1). Given their high scattering efficiency, silicon nanowires can be seen in low magnification using either dark- or bright-field microscopy. Furthermore, since they do not require fluorescence staining, fluorescence measurements can be reserved for orthogonal measurements. In addition, they are synthesized in one-step via the vapor–liquid–solid growth mechanism using a chemical vapor deposition system to display a wide range of lengths, morphologies,[7−9] and thicknesses, from a few nanometers to a few micrometers. Most importantly, the option to have a narrow (i.e., small thickness) nanowire significantly expands our experimental toolset because it makes the probe sensitive to small mechanical perturbations, as shown in the nanowire’s cellular uptake[10] and intercellular force study.[11]

In our method, a short arm (structural asymmetry) is grown at the end of a straight nanowire to serve as a marker in tracking the wire’s longitudinal orientation (θ). As the nanowire rotates along its long axis, the projected length of the arm (PLarm) on the microscope detection plane changes according to eq , where θ = 0° is defined as the orientation in which the arm lies parallel to the detection plane (Figure ).

While the projected length of the arm varies according to the θ, the actual length of the arm (l) and the apparent radius of the nanowire (r) are measured constants (Supporting Information S2). Longitudinal orientations are obtained by solving eq .

In this paper, we first introduce our newly developed particle detection algorithms that can precisely and efficiently detect the projected lengths of the arm (PLarm). Then, as a proof of concept, we apply our technique to study the longitudinal rotation of a kinked nanowire floating in media with no cell contact and a cell-interacting kinked nanowire. We demonstrate that while the nanowire exhibits thermally activated (i.e., Brownian) random rolling motion in solution, the nanowire exhibits super- and subdiffusive rolling motions when in contact with a mammalian cell.

We developed nanowire detection algorithms with two key components to measure the projected length of the nanowire arm (PLarm). First, we built a subpixel fitting algorithm to precisely resolve the nanowire center with nanometer precision, and second, we used principal component analysis (PCA) to segment the nanowire into the main body and arm. In the first step, a custom MATLAB and Python subpixel fitting algorithm was developed, named Gaussian centerline detection. The algorithm was inspired by single molecule localization techniques.[12] We reasoned that similar techniques could be used to detect the center of a nanowire, which is also a subdiffraction-limited object in its longitudinal dimension. Additionally, we adopted a line filter tool, which was inspired by retinal blood vessel detection, to determine the direction normal to the nanowire (Figure B).[13] The line fit with the narrowest Gaussian represented the best normal direction to the nanowire. We assigned the center of the Gaussian fit to be the true center of the nanowire. In this step, we greatly improved the accuracy of the PLarm detection in the next step (Figure S2) and increase the utilized portion of the data (Figure S3, Table S1).

Figure 2

Particle detection algorithms. (A–C) Demonstration of the Gaussian centerline detection algorithm. (A) Optical microscope image of a kinked silicon nanowire (in color, based on the intensity) with the detected Gaussian centerline (red) overlay. Around each bright pixel, we selected a subimage (red box) and applied the line filter algorithm. (B) Zoomed-in image of area marked by the red box in (A). The threshold-selected bright pixel (black dot) is fitted to a center (black star); 30-pixel long intensity profiles (dotted lines) centered on the coordinate of interest are fitted to their centers (red dot) every 30°; and the selected intensity profile line (red) is roughly perpendicular to the nanowire main body. (C) Normalized intensity profiles (dots) along the lines in (B) and their Gaussian-fitted lines (solid lines). The selected profile and fitted line are in red. (D–F) Demonstration of the PCA-based segmentation algorithm. (D) Middle section of the Gaussian-selected center is selected (blue) for the initial fitting of the PC1. (E) Fitted results: PC1 (dotted cyan line) fits the main body part based on the blue region. PC2 (dotted magenta line) fits the arm part based on the red region. (F) The three coordinates (armend, kink, main bodyend) are selected based on PC1 and PC2.

In the second step, we built another custom Python algorithm, PCA-arm detection, to automatically segment the nanowire into the main body and the arm by fitting the coordinates from the Gaussian centerline detection algorithm to principal component 1 (PC1) and principal component 2 (PC2), respectively. Initially, we used a subgroup of coordinates near the centroid to fit the main body with PC1. We improved the selection of the main body by reselecting the subgroup based on the initial PC1, refitting the PC1, and repeating these steps twice to ensure accuracy. Next, we used the remaining coordinates to fit PC2 in a similar fashion. Finally, we determined the PLarm, by measuring the distance from the arm end point to PC1. Detailed image analysis processing is described in the Supporting Information, Tables S2 and S3.

To test the sensitivity of our tracking tool in a neutral setting, we let the nanowire float in a two-dimensional cell culture, where the nanowire had no interaction with the cell (Video S1). As it is crucial to have our nanowire stay in the focal plane of the microscope, we let the nanowire settle near the bottom of the substrate, where the out-of-plane rotation or z-axis translocation of the nanowire main segment is minimized (Supporting Information (Methods and Materials)). We quantified the nanowire’s rotational dynamics by fitting the mean squared angular displacements in the longitudinal axis (MSADlongitudinal) to a power function (eq ) with the anomalous exponent (α) and the diffusivity coefficient (D) (Figure C,D).where θ0 is the longitudinal orientation of the nanowire at a reference frame, and θ(t) is that at a time t from the reference frame.

Figure 3

Extracting the rolling motion from the raw data. (A) PLarm vs time plot from the non-interacting nanowire experiment; 100 data points (green box) are used to demonstrate how they are processed in (B) and (D). (B) PLarm (black) and longitudinal orientation (green) vs time plot of the 100 data points. (C) Anomalous exponent (red) and diffusivity coefficient (blue) vs time plots of the entire data shown in (A) with their respective errors bars (magenta, cyan). (D) MSADlongitudinal vs lag time of the 100 data points.

The non-interacting nanowire (Figure , Figure S4, Video S1) showed a rapid and random rolling motion as characterized by the large diffusivity coefficient throughout the video (Figure C, Video S1). As expected, the rolling motion was much more conspicuous than the nanowire’s translational or in-plane rotational motions. The predominantly subdiffusive (i.e., α < 1) rolling motion may be due to the movement of the nanowire in and out of the extracellular matrix or a no slip boundary condition. The variation in the anomalous exponent shown in Figure C suggests that the nanowire was positioned in an inhomogeneous environment.

Next, we investigated the probe’s ability to detect force from its environment by tracking the rolling motion of the nanowire upon interaction with a human umbilical vein endothelial cell (HUVEC), which is known to internalize silicon nanowires.[10] For the purposes of demonstrating our new method, we were interested in probing how the cellular behavior affects the probe’s rolling dynamics. Based on the fact that the nanowire did not overlap with the cell’s nucleus when fully encompassed (Videos S2, S3, and S4) and HUVEC’s tendency to internalize silicon nanowires,[10] we assume that the probe was internalized by the cell as opposed to lying on the membrane outside the cell. From its first contact with the cell to its complete internalization by the cell, the nanowire displayed a variety of longitudinal rotational behaviors, which were sequentially categorized into three phases: contact, static, and dynamic. In the contact phase (0–8 min), the cell and the nanowire had their initial contact at the end of the nanowire’s main body (Figure B(i)). The cell then encompassed the nanowire’s main body, and subsequently the nanowire arm (Figure B(ii–iv)). In the static phase (8–42 min), once the nanowire was completely internalized, it displayed a negligible amount of longitudinal rotation. This static phase persisted for about 80 min. In the dynamic phase (110–122 min), the cell vigorously contracted and expanded, which induced the nanowire to roll (Videos S2, S3, and S4).

Figure 4

Nanowire–cell interacting experiments. (A) Longitudinal orientation vs time plots of three sequential experiments of the same nanowire interacting with the same cell. (B) Time series of optical microscope images; falsely colored are the cell (yellow) and the nanowire (pink). Note that the nanowire underwent in-plane orientation and translocated within the cell over the 70 min period between viii to ix during when the cell gradually moved and its membrane ruffled. Scale bar: 4 μm. (C) Anomalous exponent (red) and diffusivity coefficient (blue) vs time plots for the cell-interacting parts. Errors (magenta for anomalous exponent fitting error, cyan for diffusivity coefficient fitting error) are reported. Color blocks highlight different cellular behaviors: cell encompassing the nanowire main body (yellow), cell encompassing the nanowire arm (blue), cell contracting (green), cell expanding and migrating (purple). Roman numerals in (A–C) indicate the same time points.

In the static phase, the nanowire maintained an orientation, where its arm lay parallel to the cell culture substrate (i.e., 180°). In contrast, in the contact and dynamic phases, the nanowire underwent unidirectional super diffusive rolling motions (Figure ). For example, in the contact phase, the anomalous exponent of the MSADlongitudinal increased to 1.61 ± 0.04. The observed active rolling of the nanowire is reminiscent of the active in-plane rotation of a Au nanorod observed during its endocytosis reported by Chen et al.,[14] suggesting the role of angular reorientation of the particle during the internalization process. In the dynamic phase, the nanowire also displayed a roughly unidirectional rotation, with the maximum anomalous exponent reaching 1.69 ± 0.05 upon cell contraction/expansion and migration. While the nanowires displayed randomness in rotational direction in every step for both experiments, the cell-interacting nanowire rolled much more slowly than the non-interacting nanowire, as shown by the cell-interacting nanowire’s diffusivity coefficients, which were 2–3 orders of magnitude smaller. The extreme sluggishness observed can be explained by the probe being stuck on the substrate at first (Figure (i)) then by being inside the crowded cytoplasmic network.[15]

We have demonstrated that our nanowire is a uniquely sensitive motional probe, which can potentially be used to measure torque acting on nanoparticles. Similar to the rotational probes used for measuring the DNA mechanics,[16] one can calculate the associated rotational inertia (Supporting Information S1) of microscopic particles based on their rolling dynamics with an additional parameter, the nanowire thickness. The thickness can be measured by taking the scattering spectrum as demonstrated in Figure S5.[17]

Depending on the system of interest, one can leverage the synthetic flexibility of crystalline silicon nanowires by tailoring the structural parameters, i.e., the length of the main body, the length of the arm, thickness of the nanowire, and the angle between the arm and the main body. For example, thin short nanowires offer greater sensitivity and locality than longer and thicker nanowires; however, thin nanowires can be bent even by intracellular forces,[11] which may complicate the interpretation of the rolling motion. It should be noted that the arm itself could alter the dynamics of the nanowire, as it is not an innocent observer. A large enough arm will cause the rolling motion of the nanowire to deviate from its straight counterpart and therefore introduce artifacts. In our nanowire–cell interaction experiment, the arm of the probe caused the probe to remain predominantly in the 180° orientations where the arm stayed parallel to the substrate (Figure A). In a two-dimensional culture, HUVECs are 3.5 μm thick at most near their nuclei and spread as thin as 200 nm at their peripheries.[10,18] Given the 1.7 μm long arm, the nanowire would have had no room to keep its arm upright near the cell periphery. In contrast, when the cell contracted drastically in the beginning of the dynamic phase (Video S4), the nanowire started to roll conspicuously as the bulged up interior of the cell provided enough space for the arm to roll around inside the cell. When the cell expanded again, thus flattening out, the nanowire went back to its parallel longitudinal orientation (i.e., near 0°).

The ability of our probe to reflect different cellular behaviors (e.g., nanowire internalization, contraction, expansion) suggests its potential use in different fields, including biophysics, hydrodynamics, and self-assembly. As a biological example, when studying the health effects of airborne particulate matter, the particulates’ rotational dynamics in different parts of the body such as the mucus lining of the lungs, the bloodstream, and in individual cells will affect how the particulates translocate, accumulate, and are processed by the human body.[19,20] Within the field of self-assembly, researchers have tracked the translational diffusion dynamics of particles to determine how the interparticle forces play a role in different organizational processes.[21] It stands to reason that when studying the assembly processes of anisotropic particles, whether the anisotropy is in the particles’ surface makeup or structure, researchers can now track particles’ longitudinal rotational diffusion and assess their role in interparticle dynamics and self-assembly. In fact, rolling motions played an integral role for ferromagnetic colloids that collectively show flocking and vortex phenomena.[22−24]These proof-of-concept demonstrations now open the door for in-depth studies on nanoparticle–cell interactions with statistically significant sample sizes to draw biophysically relevant conclusions. For example, the unidirectional rolling motion in the contact phase (Figure ) suggests that endocytotic mechanisms may exhibit rolling motions, which may either be due to cytoskeleton mechanics or perhaps rotations in membrane receptors.[25] Finally, while not shown in the current paper, the method can be extended to nonliving systems, such as for studying emergent phenomena of active matter[24,26] and nanoscale fluid dynamics, or applied as a general nanoscale probe of torque. To this end, we envision incorporating both convolutional and recurrent neural networks into our particle detection algorithm to enable multinanowire detection.

In this work, we have presented a new method of tracking nanoscale rolling motion using a kinked-nanowire. We developed the Gaussian centerline detection algorithm and utilized PCA to detect the longitudinal rotation of the nanowire efficiently and precisely. In our non-interacting experiment, we observed how predominant longitudinal rotation is among other rotational and translational motions. And in the cell-interacting experiment, we demonstrated the probe’s sensitivity to impart changes in a cellular environment. Given the biocompatibility,[10,27,28] the broad structural diversity, and the simple experimental setup, we believe our kinked silicon nanowire method will better equip researchers across many fields.