Microscopic motility of isolated E. coli flagella

The fluctuation-dissipation theorem describes the intimate connection between the Brownian diffusion of thermal particles and their drag coefficients. In the simple case of spherical particles, it takes the form of the Stokes-Einstein relationship that links the particle geometry, fluid viscosity, and diffusive behavior. However, studying the fundamental properties of microscopic asymmetric particles, such as the helical-shaped propeller used by $\textit{E. coli}$, has remained out of reach for experimental approaches due to the need to quantify correlated translation and rotation simultaneously with sufficient spatial and temporal resolution. To solve this outstanding problem, we generated volumetric movies of fluorophore-labeled, freely diffusing, isolated $\textit{E. Coli}$ flagella using oblique plane microscopy. From these movies, we extracted trajectories and determined the hydrodynamic propulsion matrix directly from the diffusion of flagella via a generalized Einstein relation. Our results validate prior proposals, based on macroscopic wire helices and low Reynolds number scaling laws, that the average flagellum is a highly inefficient propeller. Specifically, we found the maximum propulsion efficiency of flagella is less than 5%. Beyond extending Brownian motion analysis to asymmetric 3D particles, our approach opens new avenues to study the propulsion matrix of particles in complex environments where direct hydrodynamic approaches are not feasible.Comment: 6 pages, 4 figures, 9 supplemental sections, 7 supplemental figures, 3 supplemental movies *authors contributed equally and reserve the right to change order for first authorshi

RZC purification of high and low aspect ratio DNA origami nanostructures.

(A) 3D rendered model of high aspect ratio 6-helix bundle DNA origami nanotube (6-hb) monomers. (B) Gel result of liquid fractions from top to bottom (fractions 1–17) of the 6-hb sample. R is unpurified samples as a negative control lane. Fractions 14 and 15 correspond to the fractions containing the purified monomers. (C− F) AFM images and their corresponding heigh distribution of 6-hb monomer before (C and E) and after (D and F) RZC purification. (G) RZC purified 6-hb monomer SYBR gold stained 6-hb monomer sample after RZC purification. (H) 3D rendered model of a 40-nm DNA origami snub cube (SC). (I) Gel shift assays for indicated RZC-purified SC samples using glycerol gradients prepared by overnight passive diffusion or LEGO gradient mixer, followed by ultrafiltration.</p

Glycerol gradient preparation and RZC purification (S1 Movie in S1 File).

(A) Preparation of glycerol gradient with LEGO gradient mixer and separation of sample by RZC. (B) Layers of glycerol before mixing; the blue glycerol at the bottom is 45% (v/v) and the clear glycerol at the top is 15% (v/v). (C) Linear glycerol gradient after mixing with LEGO gradient mixer. (D) 140 nm green fluorescent beads on top of the glycerol gradient before RZC. (E) Fluorescent beads after RZC concentrated into a thin layer due to separation from the glycerol gradient. All glycerol solutions were diluted in 1× TAE 12.5 mM MgCl2.</p

Comparison of different spin time for different gradients.

(A–D) Four different combinations of glycerol concentrations before and after loading into the LEGO gradient mixer. The bottom layer of glycerol is dyed blue for visual inspection, while the top layer is left clear. Four spin times were selected to compare the glycerol gradient formed at the indicated spin times. As can be seen by the color gradient created as the blue-dyed glycerol mixes with the clear glycerol, each gradient, and spin time combination lead to comparable results.</p

Fig 1 -

Side view of the LEGO gradient mixer during (A) its initial position and (B) its horizontal tilting phase. (1) 3D printed centrifuge-tube holder. (2) Spinning motor to rotate the tubes while in horizontal position. (3) Turning servo motor responsible for tilting the tubes horizontally. (4) Large grey gear connecting the two motors with its small gear complement. (5) The scaffold holding the structure together. (6) The LEGO controller for orchestrating the motions of the two motors. The black cables are traced in white for clarity.</p

RZC purification of 6-hb dimer.

(A) 3D-rendered model of a 6-hb dimer. (B) Comparison between SYBR gold stained 6-hb monomer (left) and (C) 6-hb dimer (right) purified using a 30%—60% gradient column centrifuged for 3 hours at 50k rpm in 4°C. (D) SYBR gold stained dimer with 6 hours of centrifugation. (E) AFM image of unpurified dimer. (F) Precursor monomer (highlighted blue) and dimer (highlighted light brown) from unpurified dimer. (G) AFM image of RZC purified dimer. (H) Significantly smaller number of monomer (highlighted blue) with similar number of dimer (highlighted light brown) compared to those in unpurified dimer. (I and J) Comparison of precursor monomers (highlighted blue) and dimer (highlighted light brown) between unpurified and purified dimer. Dimer content of unpurified dimer and purified dimer at 21±5% and 63±6% respectively. Standard deviation was calculated with the bootstrapping method (N=273 for unpurified dimer; N=114 for purified dimer).</p

This document provides comprehensive supporting information, including detailed protocols, materials, equipment, 5 supplementary figures, 2 supplementary tables, and 1 supplementary movie.

This document provides comprehensive supporting information, including detailed protocols, materials, equipment, 5 supplementary figures, 2 supplementary tables, and 1 supplementary movie.</p