Supplementary Data. Resolving Rotational Motions of Nano-objects in Engineered. Environments and Live Cells with Gold Nanorods and

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1 Supplementary Data for Resolving Rotational Motions of Nano-objects in Engineered Environments and Live Cells with Gold Nanorods and Differential nterference Contrast Microscopy Gufeng Wang, Wei Sun, Yong Luo and Ning Fang* Ames Laboratory-USDOE and Department of Chemistry, owa State University, Ames, owa, 5 These authors contributed equally to this work. *To whom correspondence should be addressed. nfang@iastate.edu. S

2 THEORY. DC principles and imaging of optically isotropic nanoparticles DC microscopy works on the principle of interference to gain information about differences in refractive index and optical path length of specimen components. A Nomarskitype DC microscope contains Nomarski prisms. The incident light is split by the first Nomarski prism into two orthogonally polarized, laterally shifted beams for illumination. For non-absorbing, optically isotropic samples, two identical intermediate images with different polarizations form behind the objective, each with a flat intensity profile but a curved phase profile. The two identical images are shifted and summed in the presence of the second Nomarski prism to generate the interference pattern of the final DC image. Specifically, when a non-absorbing, isotropic nanoparticle that has a diameter smaller than the shear distance ( x) is on the object plane, the phase profiles of the two intermediate images are the same. Without losing generality, assume the image polarized along the y-direction was laterally shifted x by the second Nomarski prism toward the negative direction of the x-axis, and the image polarized along the x-direction was shifted x toward the positive direction. Assuming a perfect point spread function for the optical system (the Delta function), the brightest and the darkest intensities in the final image will appear at - x and + x, where the phase difference between the two mutually shifted images assumes the peak values + γ and γ. γ is the phase delay of the illumination beam caused by the nanoparticle: πl γ = n λ, (A) S

3 where L is the optical path (in this case the particle diameter); λ is the wavelength of the incident beam; n is the refractive index difference between the nanoparticle and the surrounding medium. The amplitude of the electric vector at - x and + x in the final image plane are: E = E[ e e iγ iθ iθ x, e ] (A) E iθ iγ iθ = E[ e e e ]. (A3) + x E is the amplitude of the electric vector of one of the two illumination beams on the object plane and the intensity of the two illumination beams are assumed to be the same. θ is an additional phase bias introduced by the manufacturer of the microscope to give an optimal image contrast. The amplitude of the electric vector in the background is: E b = E[ e e iθ iθ ]. (A4) By adjusting the phase bias θ to be 9 o, the DC image of an isotropic sphere can be tuned to show even bright and dark parts, and the relative bright and dark intensities are calculated by the following equations: x = + sinγ, (A5) x = sinγ. (A6) +. Optically anisotropic nanoparticles and their DC images The gold nanorods used in the paper have a dimension of 5 73 nm. The plasmon resonance wavelengths of these gold nanorods are at 5 nm and 78 nm, respectively (Fig. c). S3

4 The maximum DC contrasts appear at wavelengths slightly red-shifted to the corresponding plasmon resonance wavelengths, which is consistent with the Kramers-Kronig relations. One special characteristic of gold nanorods is that their plasmon resonance modes are aligned with their geometric profiles: one along the long axis (longitudinal mode) and the other along the short axis (transverse mode). This results in wavelength-dependent anisotropic refractive indices of the gold nanorods. When a gold nanorod is imaged under a DC microscope, the phase delays on the two polarized, intermediate images are different, resulting in uneven bright/dark images of gold nanorods. n fact, the phase delay caused by the nanorod depends on the angle between the optical axis of the nanorod and the corresponding polarization direction of the illumination beam. For example, when the nanorod is illuminated at 7 nm and is oriented so that its corresponding optical axis (the long axis) is perfectly in line with the y-axis direction, it generates the largest phase delay (determined by the extraordinary refractive index n e ) on the image polarized in the y-direction and the minimum phase delay (the ordinary refractive index n o ) on the other image polarized in the x-direction. The DC image of the gold nanorod will have the highest bright intensity ( ) and the lowest dark intensity ( ), resulting in a mainly bright spot in the DC image. Similarly, when the nanorod is rotated to align with the x-axis direction, the result is a mainly dark spot in the DC image. At any angle in between, both the dark and bright parts with different proportionalities are observed. (See Supplementary Fig. for illustrations.) n this paper, the optimal observation wavelengths were selected to be 54 nm and 7 nm for individual gold nanorods. Apparent periodicities of 8 were observed at these two wavelengths. n D and 3D orientation determination, 7 nm illumination was used. Kreibig, U.; Vollmer, M. Optical Properties of Metal Clusters, Springer Series in Materials Science, Vol. 5; Springer: New York, 995; Vol. 5. S4

5 3. Determination of the D orientation angle φ The periodic change provides an opportunity to determine the j n e p absolute orientation of a gold nanorod. When the phase bias θ is adjusted to be 9 o, the bright intensity in a nanoparticle DC image is the result of the interference between the phase-delayed y-polarization y n o φ x s k image and the non-phase-delayed x-polarization background. Correspondingly, the dark intensity is the result of the overlay between the phase-delayed x-polarization image and the non-phasedelayed y-polarization background. For the illumination beam that is polarized in the y-direction, it can be decomposed into two orthogonal components, with electric vectors perpendicular and parallel to the corresponding optical axis of the nanorod, respectively: E = pe sinφ + s cosφ. (A7) E After passing through the sample plane, the two components will be delayed to different extent due to the optical birefringence of the nanorod: iδ E = pe sinφe + se cosφe iδ, (A8) where δ = (n e -n m )πl/λ and δ = (n o -n m )πl/λ; n e and n o are the extraordinary and ordinary refractive indices, respectively; n m is the refractive index of the medium; L is the optical path in sample (the nanorod s short axis). Projecting back to the original coordinates: E iδ iδ iδ iδ = je (sin φe + cos φe ) + ke cosφ sinφ( e + e ). (A9) Due to the working principle of the Nomarski prism, the electric vector polarized in the x- direction does not contribute to the interference pattern of the sample image (Supplementary Fig. b) and can be ignored: iδ (sin cos iδ E = je φe + φe ). (A) S5

6 The electric vector of the y-component after the second polarizer can be written as: E y = iδ iδ je (sin φe + cos φe ). (A) Correspondingly, the electric vector of the x-component at the same location is: E x = ke. (A) The electric field is the summation of Eq. A and A with an additional phase bias θ: iδ iδ iθ E x = E(sin φe + cos φe ) e E The intensity at the interference point is: e iθ. (A3) sin 4 (θ + δ) 4 x = E x = E [sin φ sin + cos φ sin (θ + δ) (θ + δ ) ( δ ) φ cos φ sin sin cos ]. (θ + δ δ ) + (A4) Similarly, the background E b can be derived as: iθ iθ Eb = Ee Ee and the background intensity b is: b b =, (A5) = E E sin θ. (A6) When the phase bias θ is set at 9, the relative DC intensity of the bright part is: x b = sin φ sinδ + cos φ sinδ + sin φ cos φ[cos( δ δ ) + sinδ + sinδ ]. (A7) Eq. A7 gives the analytical solution of the DC intensity as a function of the orientation angle φ. n practice, we found that applying a large birefringence approximation, we can simplify Eq. A7 to a sin 4 φ relationship while maintaining satisfactory results for φ greater than 3 : S6

7 x b 4 = x b = sin φ sinδ b b. (A8) At φ = 9, the intensity is at its maximum value, that is, - x = p. x b p p b max = = = sinδ b b b. (A9) Take the ratio of Eq. A8 and A9: max 4 sin φ. (A) Rearrange: φ = asin( / ) / 4, (A) max thus, φ can be determined from the bright part of the DC image, where and max are defined in Fig. d. Considering the sin 4 relationship, the relative brightness ( / max ) of the nanorod image can be viewed as a measure of the projection of the nanorod onto the y-polarization direction. The large birefringence approximation requires that δ is large (sinδ approaches ), while δ is close to. The rationale is given below. For a noble metal spheroid, the phase delay δ due to the extraordinary refractive index n e is usually much larger than the phase delay δ due to the ordinary refractive index n o. Under this condition, Eq. A7 gives a periodical relative intensity as a function of φ with a minimum relative intensity equals to + sinδ. From the experimentally collected rotation data of 5 73 nm gold nanorod (Fig. d), we know that the relative background intensity ( b ) is ~.3, so sinδ.3 and δ.7. Thus, all δ and sinδ can be ignored from Eq. A7. Rearranging Eq. A7, we have: b 4 = sin φ sinδ + sin φ cos φ(cosδ + sinδ). (A) S7

8 When sinδ is large (approaching ), Eq. A can be reduced to sin 4 φsinδ (Eq. A8). When sinδ is small, Eq. A can be reduced to sin φsinδ. Under our experimental conditions, the 5 73 nm nanorod gives a fairly large phase delay δ at 7 nm illumination. The Ι/ max curve is closer to that of the sin 4 φ model by showing a large flat region at the lower portion of the curve (Fig. d). Also, the calculated angles using the sin 4 φ model are consistent with physically rotated angles, showing a linear correlation at most angles (Supplementary Fig. 3a). Thus, using Eq. A8 instead of A7 in determining the orientation angle is valid. The errors of the angle determination can be estimated from: σ φ φ φ φ =. (A3) ( ) σ + ( ) σ p + ( ) σ b p b The standard deviations of measured (σ ), maximum (σ p ), and background (σ b ) intensities are all on the same level due to the high background of DC microscopy. Supplementary Fig. 3b shows the standard deviation of the measured orientation angles from the 7 nm bright curve in Fig. d. The relative error of the intensity measurement was ~.5% for the immobilized nanorods submerged in water. Above 3, the recovered angle φ is satisfactory, with a standard deviation less than. between 3 ~8. Below 3, the signal becomes too weak due to the sin 4 φ relationship. Similarly, φ can also be determined from the dark part of the DC image: ' ( ' / ) / 4 φ = acos, (A4) max and the relative darkness ( / max ) of the nanorod image can be viewed as a measure of the projection of the nanorod onto the x-polarization direction. When the nanorod is lying in the object plane, the dark part yields the same information about φ but that it gives better signals at φ between below 6 (Supplementary Fig. 3cd). Combine Supplementary Fig. 3a and 3c to give S8

9 Supplementary Fig. 3e, which demonstrates the satisfactory angle determination in nearly the entire range. The relative error of the angle determination is undoubtedly relevant to the precision of the intensity measurement. n above discussion (Fig. d and Supplementary Fig. 3a-d), the precision of the intensity measurement was ~.5% for the immobilized nanorods submerged in water. At this noise level, the standard deviation is ~ in the range of 3-8 from the bright part using Eq. A (Supplementary Fig. 3b) and -6 from the dark part using Eq. 4 (Supplementary Fig. 3d). Thus, using both the bright and dark parts, we can resolve the D orientation of immobilized nanorod with ~ resolution in nearly the entire range (-8, Supplementary Fig. 3e). When the nanorod is used to probe dynamics inside live cells, the background becomes noisier. n the current setup for live-cell imaging, an exposure time of.3 s was used to image both the cells and the gold nanorod probes. The relative error of the intensity measurement was found to be less than.5%, resulting in a standard deviation of less than 3. Note that max and max for each individual nanorod must be calibrated before the absolute orientation angles can be calculated from live-cell images. The current strategy is to follow the same nanorod for a long period of time, and the averages of the brightest intensities and the darkest intensities out of several thousand images are treated as max and max, respectively. 4. 3D orientation and rotation pattern of a nanorod When the nanorod s long axis is pointing toward outside of the image plane, an additional variable - the elevation angle ψ - is needed to determine the 3D orientation of the nanorod. The illumination beam S9 y ψ φ x

10 polarized at the y-direction can be decomposed in a similar way: E = pe sinφ + s cosφ, (A5) E where p- and s- directions are defined according to the projection of the nanorod on the image plane. The optical path will be longer than that of the rod lying in the image plane. For a spheroid, the new optical path is: a b L =, (A6) a sin ψ + b cos ψ where a and b are the short axis and the long axis of the spheroid, respectively. For the s- component of the electric vector, it will be delayed according to the ordinary refractive index n o. The phase delay of the s-component of the electric vector δ is: ' δ δ b =. (A7) a sin ψ + b cos ψ For the p-component of the electric vector, the propagation velocity of the light is a function of the angle between the wave propagation direction and the optical axis of the nanorod: v = v sin ψ + v cos ψ, (A8) p o e where v o and v e are the velocities of the ordinary wave and the extraordinary wave, respectively. Thus, the phase delay of the p-component of the electric vector is: ( ' δ = δ neno nm) n sin ψ + v cos ψ e o n n e m b a sin ψ + b cos ψ. (A9) Two special cases: () When ψ =, δ = δ, and δ = δ. This situation is equivalent to the nanorod in the image plane and has been considered in Theory Section 3. () When ψ = 9, δ S

11 = δ = δ b/a. Under this condition, the particle is standing straight on the image plane and shows even bright and dark parts in the DC image as an isotropic particle. After passing through the sample plane, the two electric vector components (p and s) will be delayed to different extent due to the optical birefringence of the nanorod: E = ' iδ pe sinφe + se cosφe ' iδ, (A3) where δ and δ are determined from Eq. A7 and A9. Using the similar treatment of Eq. A8-A, we can reach Eq. A3 to characterize the relative intensity of DC image: b 4 ' ' ' = sin φ sinδ + sin φ cos φ(cosδ + sinδ ). (A3) The fraction of the relative intensity to the overall maximum intensity (when the nanorod is perfectly aligned with the y-polarization and in the image plane) is: max 4 ' ' ' sin φ sinδ sin φ cos φ(cosδ + sinδ ) = + sinδ sinδ (A3) Taking a similar approximation as in the Theory Section 3: max 4 ' sin φ sinδ =. (A33) sinδ Similarly, we can get the formula for the intensity for the dark part of the DC image. ' ' max 4 ' cos φ sinδ =. (A34) sinδ n theory, when the max and max for each nanorod are properly calibrated, we are able to determine the 3D orientation angles φ and ψ from each DC image of the nanorod. Thus, we can track the nanorod movement in five dimensions (5D): three spatial coordinates and two orientation angles. S

12 n practice, the current instruments only provide enough signal-to-noise ratios for accurate determination of 3D orientation angles within a limited range. n the present work, we demonstrate that the characteristic rotational motions of the nanorod can be identified from a series of DC images even though the exact orientation of the nanorod at a given moment cannot be determined accurately. S

13 SUPPLEMENTARY FGURE LEGENDS Supplementary Figure. The TEM image of 5 73 nm gold nanorods used in this work. Supplementary Figure. DC imaging schemes of anisotropic nanoparticles. (a) The origin of disproportionate bright and dark parts for DC images of gold nanorods. (b) llustration to show that the extra polarization component introduced by optical birefringence of the gold nanorod is not contributing to the DC image of the nanorod. Detailed discussions can be found in the Theory section of this Supplementary Data. Supplementary Figure 3. Orientation determination in D. The calculations are based on the data plotted in Fig. d. (a) Orientation angle φ determined from the bright part of the DC images at 7 nm. The determined angles are satisfactory for φ > 3 o. (b) Estimated standard errors for φ based on a.5% relative standard deviation of DC intensity measurement. (c) φ determined from the dark part of the DC images at 7 nm. The determined angles are satisfactory for φ < 6 o. (d) Corresponding standard errors for (c). (e) φ determined using both the bright and dark parts. The orientation angles are determined satisfactorily in nearly the entire range. Supplementary Figure 4. Simulated DC intensity changing pattern when a microtubule carrying a nanorod is transported toward different directions. (a) The transport direction is along the bright axis (β = ). The seven windows correspond to the nanorod binding angle α =,,.5, 45, 67.5, 8, and 9, respectively. (b) The transport direction is.5 away from the bright axis (β =.5 ). (c) The transport direction is along the bisection of the bright and dark axes (β = 45 ). (d) The transport direction is 67.5 away from the bright axis (β =67.5 ). (e) The transport direction is along the dark axis (β = 9 ). S3

14 Supplementary Figure 5. Presumed nanorod binding position to the microtubule in Figure 4. The nanorod gives a relatively smaller projection on the bright axis at the two ends of the trace while gives a larger projection on the bright axis in the middle. This is consistent with the experimental DC intensity, which shows a brighter image in the middle of the trace (Figure 4). S4

15 MOVES All movies are acquired and played at video rate (3 fps). Movie. Fluorescently tagged microtubules were transported on kinesin-coated glass substrate. Movie. Corresponding movie of Fig. 3. The gold nanorod was carried by a gliding and rotating microtubule advancing at a direction of β 6. The DC intensity showed a typical alternative bright-dark pattern. Movie 3. Corresponding movie of Fig. 4. The gold nanorod was carried by a non-rotating microtubule at a moving direction of β 66. The rod moved ~ 5 µm and the DC intensity did not show a periodical changing pattern. Movie 4. Corresponding movie of Fig. 4. The gold nanorod was carried by a non-rotating microtubule at a moving direction of β 66. The rod moved ~ 5 µm and the DC intensity did not show a periodical changing pattern. Movie 5. Cargo transport in a live cell. A nanorod-containing vesicle was transported on the microtubule network as shown in Fig. 5. The gold nanorod kept a fixed angle with the microtubule tracks even when it was being transported from one microtubule to the other. S5

16 Supplementary Figure

17 a) Supplementary Figure a

18 b) Side view microscope Top-view wave front E nd Polarizer nd Nomarski E Specimen E st Nomarski st Polarizer Supplementary Figure b

19 a) c) Bright Dark red Angle( o ) Measu b) Rotation Angle ( o ) Measu red Angle( o ) d) Rotation Angle ( o ) Error ( o ) 5 Error ( o ) At Actual langle ( o ) Actual Angle ( o ) Supplementary Figure 3a-d

20 e) ngle( o ) Measured A Rotation Angle ( o ) Supplementary Figure 3e

21 a) = o = o =.5 o = 45 o = 67.5 o = 8 o = 9 o = o in all these cases Supplementary Figure 4a

22 b) = o = o =.5 o = 45 o = 67.5 o = 8 o = 9 o =.5 o in all these cases Supplementary Figure 4b

23 c) = o = o =.5 o = 45 o = 67.5 o = 8 o = 9 o = 45 o in all these cases Supplementary Figure 4c

24 d) = o = o =.5 o = 45 o = 67.5 o = 8 o = 9 o = 67.5 o in all these cases Supplementary Figure 4d

25 e) = o = o =.5 o = 45 o = 67.5 o = 8 o = 9 o = 9 o in all these cases Supplementary Figure 4e

26 Bright Axis Dark Axis Supplementary Figure 5