Multiplexed Nanometric 3D Tracking of Microbeads Using an FFT-Phasor Algorithm

Thomas B Brouwer,Nicolaas Hermans,John Van Noort

doi:10.1016/j.bpj.2020.01.015

Abstract

Many single-molecule biophysical techniques rely on nanometric tracking of microbeads to obtain quantitative information about the mechanical properties of biomolecules such as chromatin fibers. Their three-dimensional (3D) position can be resolved by holographic analysis of the diffraction pattern in wide-field imaging. Fitting this diffraction pattern to Lorenz-Mie scattering theory yields the bead’s position with nanometer accuracy in three dimensions but is computationally expensive. Real-time multiplexed bead tracking therefore requires a more efficient tracking method, such as comparison with previously measured diffraction patterns, known as look-up tables. Here, we introduce an alternative 3D phasor algorithm that provides robust bead tracking with nanometric localization accuracy in a z range of over 10 μm under nonoptimal imaging conditions. The algorithm is based on a two-dimensional cross correlation using fast Fourier transforms with computer-generated reference images, yielding a processing rate of up to 10,000 regions of interest per second. We implemented the technique in magnetic tweezers and tracked the 3D position of over 100 beads in real time on a generic CPU. The accuracy of 3D phasor tracking was extensively tested and compared to a look-up table approach using Lorenz-Mie simulations, avoiding experimental uncertainties. Its easy implementation, efficiency, and robustness can improve multiplexed biophysical bead-tracking applications, especially when high throughput is required and image artifacts are difficult to avoid.

Highlights

Single-molecule techniques overcome ensemble averaging and can resolve unique and rare events at the molecular level [1]
Though we did not further investigate this difference, we attribute it to the mixed composition of these beads, which may not fully be captured in the single refraction index used in Lorenz-Mie scattering theory (LMST)
Because the 1 mm beads are better described by LMST, we used these smaller beads in the remainder of this work

Summary

Introduction

Single-molecule techniques overcome ensemble averaging and can resolve unique and rare events at the molecular level [1]. Interactions with proteins such as DNA compaction by histones in eukaryotic chromatin [6,7,8,9,10,11] and prokaryotic architectural proteins [12,13,14,15,16], supercoiling [17,18,19,20], and repair processes [21,22,23] were extensively studied with magnetic tweezers (MT), optical tweezers (OT), acoustic force spectroscopy (AFS) [24,25,26], or tethered particle motion (TPM) [13,27,28] These bead manipulation techniques have been used to quantify the mechanical properties of other biological structures such as extracellular protein collagen [29,30,31] or even entire cells [32].

Methods

Results

Conclusion