Supporting Information for. Landing Dynamics of Swimming Bacteria on a Polymeric. Surface: Effect of Surface Properties

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1 Supporting Information for Landing Dynamics of Swimming Bacteria on a Polymeric Surface: Effect of Surface Properties Meng Qi, Xiangjun Gong*, Bo Wu, Guangzhao Zhang* Faculty of Materials Science and Engineering, South China University of Technology, Guangzhou , P. R. China *Corresponding author Figure S1. Morphology, RMS roughness and the elastic modulus (E) of the surfaces measured by AFM. E for the surfaces were calculated from AFM force curves, and range from 1 to 6 MPa. 1

2 Figure S2. (a) Curves for growth of E. coli (HCB1). HCB1 were harvested at mid-exponential phase (4 h, OD 600 = 0.4) and diluted to a concentration of ~10 6 cells/ml for observation. (b) Electrophoretic mobility and zeta potential (ξ) of mid-exponential phase E. coli cells in motility buffer (MB, 10 8 cells/ml) with concentration of 10 7, 10 6, and 10 5 cells/ml. It shows that the charging on bacterium surface does not have concentration dependence. (c) ξ for motile E. coli cells at 0, 120 and 240 min and that for the dead ones. As motility decreases, E. coli tend to be more negatively charged. 2

3 Figure S3. (a) SEM image of E. coli body. (b) In-focus reconstruction DHM image of E. coli body. (c) AFM image of E. coli body together with its flagella. Observations were performed with bacteria adhered to a glass surface modified with poly-l-lysine. (d) The average size (length and width) of bacterial body was obtained by measuring over 30 E. coli cells with SEM and DHM at different time points (0, 120 and 240 min). (e) The average length of bacterial flagella bundle was obtained by measuring over 26 E. coli cells with AFM. 3

4 Figure S4. Determination of the localization accuracy of DHM. (a) Average distance of 39 immobilized polystyrene (PS) latex particles (diameter = 1 µm) from the focal plane (z) as a function of the objective displacement (d). The error bars show the standard deviation. The dashed line denotes z = d. (b) Average z error (z-d, blue) ± standard deviation (cyan) plotted against the objective displacement (d) with a binned width of 2 µm. (c) Root mean square (rms) error plotted against the objective displacement (d). In the µm defocus range where we used for 3D imaging, rms error corresponding to the localization accuracy is around 400 nm in z direction. 4

5 Figure S5. Motility of E. coli in terms of power index (υ) of mean square displacement (MSD) as a function of time. (a) Histogram of υ for dead E. coli cells which have lost motility. Average value of υ = 0.44 by Gaussian fit indicates the dead E. coli cells undergo subdiffusive motion. (b) A typical histogram of υ for E. coli cells near the PBMA surface. The distribution is bimodal and the average υ for each peak shown in the figure is given by Gaussian fit. Moreover, the percentage of subdiffusive cells can be obtained from the area of the peak with a smaller υ. 5

6 Figure S6. V 3D distribution along z direction and average V 3D from Gaussian fit of 346 motile E. coli cells recorded on PSPMA surface at 0 min. (a) V 3D distribution along z direction. It shows that most E. coli cells accumulate near the surface (red color). The digits and hollow points represent average V 3D at different regions (bottom to top: 1 µm, 5 µm, 10 µm, µm and µm). (b) Distribution of V 3D of E. coli cells on PSPMA surface at z = 1 and 10 µm extracted from (a). The average velocity is estimated to be 33.9 and 35.5 µm/s by Gaussian fit respectively. 6

7 Figure S7. V 3D distribution along z direction and average V 3D from Gaussian fit of 137 motile E. coli cells recorded on polystyrene (PS) coated surface at 0 min. (a) V 3D distribution along z direction. The digits and hollow points represent average V 3D at different regions (bottom to top: 1 µm, 5 µm, 10 µm, µm and µm). (b) Distribution of V 3D of E. coli cells on PSPMA surface at z = 1 and 10 µm extracted from (a). The average velocity is estimated to be 27.0 and 32.1 µm/s respectively. 7

8 Figure S8. Time dependence of tumbling frequency (F T ) of E. coli cells as a function of distance (z) from the surface. (a) Schematic of a tumble event. One flagella of the cell unbundles from the others causing a sudden change in the running direction. In tumble analysis, the same criteria for tumbling was used as reported before. 1 Trajectories with an average velocity higher than 20 µm/s were considered and tumbles were determined when drastic directional changes from the swimming trajectories exceeding 50 degrees. (b) 3D trajectory of a near-surface E. coli cell with tumbling (red points). A tumbling happens with a sudden drop of velocity as well as a sharp turn of swimming direction. (c) Time dependence of F T of E. coli cells near the surface as a function of z. As z decreases, F T decreases due to the surface-induced reduction in the hydrodynamic interaction for the flagella unbundling. 2 (d) F T on different surfaces. F T makes no difference in the range 0 < z 10 µm at a certain time, but it increases with time, indicating that tumbling rate decreases as E. coli approach to the surface. 8

9 Figure S9. Average collision probability of motile E. coli cells by tail (P tail, a) and head (P head, b) with the surfaces. Figure S10. Scattered angle (θ out ), scattered rotational rate (Ω out ) and the percentage of E. coli cells with the dependence of the deformation (h) colliding with the PBMA surface by tail at 0, 120 and 240 min. 9

10 Figure S11. Scattered angle (θ out ), scattered rotational rate (Ω out ) and the percentage of E. coli cells with the dependence of the deformation (h) colliding with the PBMA surface by head at 0, 120 and 240 min. Figure S12. Average scattered rotational rate (Ω out ) of motile E. coli cells colliding with the surfaces by tail as around 7 rad/s (a) and head as 12 rad/s (b) at 0 min. 10

11 Figure S13. Normalized surface attraction force (γ) between the surfaces and RP437 flic measured by AFM. Table S1. Dry, wet thickness, swollen ratio, number density (σ) of grafted chains, molecular weight (M n ) and the relaxation time (τ) of the polymeric surfaces. The measurement and estimation of parameters are presented in Supplementary Methods. Supplementary Methods Surface characterization. Dry (h dry ) and wet (h wet ) thickness of the surfaces were measured by a spectroscopic ellipsometer (M-2000V, J. A. Woollam) at two incident angles in air and fit by using the software CompleteEASE, where the polymer layer is treated as a single Cauchy layer between silica substrate and air. h wet was measured in the motility buffer at the incident angle of 75 using a liquid cell. The resultant data was fitted by a two-layer model. A silica substrate immersed in the motility buffer was 11

12 used as the background. The swelling ratio (α) is defined as h wet divided by h dry, where h dry is calculated as h = (1) N is the number of repeat units of volume (a) 3, a is the monomer size, σ is the number of chains grafted per unit surface. For acrylic monomer (HEMA, SPMA, SBMA and BMA), a is equal to the length of C-C bond as 0.58 nm. On the other hand, the grafting density σ can be estimated as α=( ) / (2) σ= (3) where d is the average distance between tethered points of neighboring polymer chains, and υ = 1/2 for densely grafted polymer chains in good solvent. For PBMA chains grafted on surfaces, σ is calculated as σ= (4) where ρ ~ 1.1 g/cm 3 for PBMA chains and M w is the weight-averaged molecular weight of PBMA chains determined by GPC as g/mol. As a result, the molecular weight (M n ) can be obtained. For polymer chains grafted on surfaces, the relaxation time τ ~ 10c 1.5 M n 2.0, where c is the bulk concentration of the polymer chains that can be obtained from h wet and σ. 3, 4 The above results were shown in Table S1. The elastic modulus (E) of the polymeric surfaces was measured by AFM. E was determined based on the Hertzian contact theory, which correlates the AFM force signal (F) to the indentation depth of the cantilever tip (δ) by: 5 12

13 = (5) ν is the Poisson s ratio and is 0.5 for all polymeric substrates. α is the face angle of the four-sided pyramidal tip of the cantilever (22 ). δ = d p - d f where d p is the AFM piezo displacement, and d f is the deflection of the cantilever free end. Characterization of physical features of E. coli. The growth curve of the wild strain HCB1 was measured as the optical density at a wavelength of 600 nm (OD 600 ) by using a spectrophotometer (model C40, Implen GmbH). Each of 13 individual tubes containing 3.0 ml of tryptone medium, was inoculated with 30.0 µl suspension of HCB1 cells in tryptone medium and cultured at 33 C and 200 rpm overnight. OD 600 for each sample was measured from 0 to 12 hrs with a time interval of 1 hour. The growth curve was acquired by conducting 2 identical measurements and getting the average values. Dead E. coli cells were acquired by mixing a mid-log phase culture of HCB1 with a 0.5 sodium hypochlorite solution (1:5 volumetric ratio). The mixture was kept at room temperature for 30 min, and suspended in MB by centrifugation. Zeta potentials (ζ) of HCB1 samples with different concentration and those which were sealed with 0, 120 and 240 min at concentration of ~10 6 cells/ml were measured in MB employing Delsa TM Nano C Particle and Zeta Potential Analyzer (Beckman Coulter) respectively. Bacterial body size in MB was measured by DHM and SEM. Poly-L-lysine (PLL) was deposited onto plasma-treated coverslips from 1.0 mg/ml aqueous solution to enhance electrostatic attraction between bacteria and substrate. At 0, 120, 240 min after dilution in MB, the bacterial suspension was deposited on PLL-modified coverslip and dried in air. In DHM measurements, 13

14 bacterial length and width can be extracted from reconstructed images of the attached cells. In SEM observation, the coverslips with attached bacteria were immersed in 2.5 % glutaraldehyde in potassium phosphate buffer at 4 C overnight to fix the cells. After fixation, the samples were washed with potassium phosphate buffer and dehydrated with increasing concentrations of ethanol (30%, 50%, 70%, 90%, 95% and 100%) at 25 o C for 10 min for each step. The dehydrated samples were coated with platinum and observed with scanning electron microscope (Quanta 200, Philips-FEI). At least 26 individual cells were measured in body length and width in both DHM and SEM measurements. The length of bacterial flagella bundle was measured by AFM (XE-100, Park Systems). PLL-modified mica sheets were soaked in a TB culture of E. coli HCB1 for 30 min to allow bacterial attachment. The samples were then rinsed with water and dried with nitrogen immediately before imaging in air. All AFM measurements were carried out in tapping mode with rectangular silicon cantilevers (NCHR, spring constant 42 N/m) at 25 C. The scanning rate was 0.05 Hz with a resolution of pixels. 26 individual cells with bundled flagella were chosen and measured. Localization accuracy of the Digital Holographic Microscopy (DHM). To determine the accuracy of localization in the vertical direction, holograms for 39 polystyrene microspheres (1 µm) immobilized on the interface of a coverslip and the motility buffer (MB) were recorded. They were imaged at varying defocus distances by vertically translating the objective motorized by a piezoelectric positioner (z-resolution: < 100 nm). 20 images were acquired from 2-40 µm defocus distances 14

15 with a step length of 2 µm. For each of these defocus images, particle distances to the focal plane (z) were acquired and plotted against the known objective displacement (d). This is shown in Figure S4a together with the standard deviations of the positions. Figure S4b shows mean z errors corresponding to the mean values of (z-d) obtained at all defocus distances with a binned width of 2 µm. Figure S4c shows the root mean square (rms) errors, where a localization accuracy of ~ 400 nm is acquired in the µm defocus range which we used for bacterial tracking. 6 Analysis of tumbling of E. coli. E. coli can rapidly change its swimming direction by unbundling flagella, which is referred to as tumbling (Figure S8). When tumbling happens, the velocity drops and the swimming direction suddenly changes. In tumbling analysis, smoothed velocities were calculated as the fourth order central difference: 8( r( ti+ t) r( ti )) ( r( ti+ 2 t) r( ti )) V ( ti ) = 12 t (6) Additionally, only trajectories that showed an average velocity larger than 20 µm/s were considered. The same criteria for tumbling detection was used as previously reported. 1, 6 Namely, a tumbling event was determined by extracting drastic directional changes from the swimming trajectories that the angle between V(t i ) and V(t i+1 ) exceeds a critical value of 50 degrees. 15

16 Supplementary Notes A. Estimation of the contributions from the friction force and propulsion Figure S14. Schematic illustrations of (a) the force acting on an E. coli cell and (b) the bending of flagella during a tail collision. R 1 and R 2 are the radius of curvature before and after bending. h is the projection of flagella deformation along the vertical direction. The bending model (Supplementary Note B) is valid when the deformation h is much smaller than the length (L) of the flagella. Friction force exerting on the bacterium by the flow is divided into rotational friction (F r ) and translational friction (F t ). F r is equal to ζω/l, where L is the flagella length for tail collision and the body half-length for head collision. The rotational drag ζ = 16

17 16πηa 2 b/3 for E. coli, 7 η of the motility medium is close to viscosity of water (10-3 Pa.s). Using the measured a = 1.3 µm, b = 0.4 µm, we have ζ = pn.µm. For tail and head collision, F r is around 0.01 and 0.1 pn which are too small comparing with the propulsion force F p. In light of the analysis by Li et.al., 8 F t which represents the hydrodynamic interactions on the bacteria can be divided into two components, F and F along and perpendicular to the orientation of an E. coli cell. At a low Reynolds number, the rotation torque balance between the body and the flagella. F and F can be described as: =( + )Ω = (7) Chattopadhyay et.al. gave the values of A 11, A 22, A 23, A 32, A 33 for a E. coli cell aligning parallel to a surface. 9 The parameters for E. coli aligning with angle θ to the surface can be expressed as A 11 =. /, A 22 =. /, A 23 = , A 32 =., A 33 = Thus, Eq. (7) can be changed as = Ω =. (8) Our measurements show that for E. coli cells colliding with the surfaces, θ out and Ω out (Figure S12) equal to 15 o and 7 rad/s (tail collision), 20 o and 12 rad/s (head collision), respectively. From velocity measurements, V ~ 35 µm/s at 0 min. Therefore, F = 2.1 (tail collision) and 3.6 pn (head collision) whereas F = 1.04 (tail collision) and 1.07 pn (head collision). From Figure S14a, the net force F net along z direction backwards the surface can be written as: 17

18 : = cos + sin cos sin : = sin sin cos + sin (9) where F e is the elastic force along the z direction regarding the flagella (tail collision) or the cell body (head collision), F s is the surface attraction force, F p is the intrinsic propulsion force (0.57 pn at 0 min). For tail collision, F p sinθ = pn, F cosθ = 2.03 pn and F sinθ = pn, which leads to a sum of the last three terms in Eq. (9) of 2.15 pn. For head collision, F p sinθ = pn, F cosθ = 3.38 pn and F sinθ = pn, leading to a sum of 3.21 pn, where the negative symbol indicates the contribution leads to attraction between the E. coli cell and the surface. If F e is known, we can obtain a minimum value of surface attraction force F s to induce adhesion of E. coli cell (F net = 0). Estimation of F e is shown as follows. B. Estimation of F e due to the bending of E. coli flagella We estimate F e induced by flagella bending in a tail collision. A bacterium is expected to recover to a more straight conformation from the configuration shown in Figure S14b where h = Lsinθ-z. The new curvature k 2 =1/R 2 in the bending state. When h << L f, we have: (10) ( ) = ( ) (11) Using θ = 15 o and h = 2 µm (z ~ 0.5 µm from Figure 8), we have k 2 = µm -1. The elastic energy U e and force F e due to flagella bending can be described as: 10 = ( ) (12) 18

19 = = ( ) (13) Therefore, = ( ) ( ) (14) Assuming the flagella is straight before collision, k 1 = 0 µm -1. The bending stiffness E = 3.5 pn.µm 2. L = 10.2 µm. L f = 8.9 µm. Based on Eq. (14), for h = 2 µm, F e is estimated to be 2.31 pn which agrees with those previously reported. 10, 11 As a result, the contributions from F e and the last three terms in Eq. (9) are comparable. F net will be larger than 0 as long as the surface force is attractive (> 0.02 pn). References (1) Berg, H. C.; Brown, D. A. Chemotaxis in Escherichia Coli Analysed by Three-Dimensional Tracking. Nature 1972, 239 (5374), (2) Molaei, M.; Barry, M.; Stocker, R.; Sheng, J. Failed Escape: Solid Surfaces Prevent Tumbling of Escherichia Coli. Phys. Rev. Lett. 2014, 113 (6), (3) Zhang, R.; Ni, L.; Jin, Z.; Li, J.; Jin, F. Bacteria Slingshot More on Soft Surfaces. Nat. Commun. 2014, 5, (4) Graessley, W. W.; Masuda, T.; Roovers, J. E. L.; Hadjichristidis, N. Rheological Properties of Linear and Branched Polyisoprene. Macromolecules 1976, 9 (1), (5) Radmacher, M.; Fritz, M.; Hansma, P. K. Imaging Soft Samples with the Atomic Force Microscope: Gelatin in Water and Propanol. Biophys. J. 1995, 69 (1), (6) Taute, K. M. High-Throughput 3d Tracking of Bacteria on a Standard Phase Contrast Microscope. Nat. Commun. 2015, 6,

20 (7) Berg, H. C. E. Coli In Motion; Springer-Verlog, (8) Li, G.; Tang, J. X. Accumulation of Microswimmers near a Surface Mediated by Collision and Rotational Brownian Motion. Phys. Rev. Lett. 2009, 103 (7), (9) Chattopadhyay, S.; Moldovan, R.; Yeung, C.; Wu, X. L. Swimming Efficiency of Bacterium Escherichia Coli. Proc. Natl. Acad. Sci. U. S. A. 2006, 103 (37), (10) Darnton, N. C.; Berg, H. C. Force-Extension Measurements on Bacterial Flagella: Triggering Polymorphic Transformations. Biophys. J. 2007, 92 (6), (11) Vogel, R.; Stark, H. Force-Extension Curves of Bacterial Flagella. Eur. Phys. J. E 2010, 33 (3),