SUPPORTING INFORMATION FOR Nanoscale Electric Permittivity of Single Bacterial Cells at GHz Frequencies by Scanning Microwave Microscopy Maria Chiara Biagi,,1 Rene Fabregas,,1 Georg Gramse, 2 Marc Van Der Hofstadt, 1 Antonio Juárez, 1,3 Ferry Kienberger, 4 Laura Fumagalli, 5 *, 1,6 and Gabriel Gomila 1 Institut de Bioenginyeria de Catalunya (IBEC), c/ Baldiri i Reixac 11-15, 08028, Barcelona, Spain 2 Johannes Kepler University Linz, Institute for Biophysics, Gruberst. 40, 4020-Linz, Austria 3 Departament de Microbiologia, Universitat de Barcelona, Av. Diagonal 643, 08028 Barcelona, Spain 4 Keysight Technologies Austria GmbH, Keysight Lab, Gruberst. 40, 4020-Linz, Austria 5 School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom 6 Departament d'electrònica, Universitat de Barcelona, C/ Martí i Franqués 1, 08028, Barcelona, Spain *Corresponding author: ggomila@ibecbarcelona.eu S1
S1. Dependence of the capacitance signal on the electric permittivity of the bacterium. Figure S1. (a) Capacitance profiles numerically calculated for different values of the bacterium relative electric permittivity in the range εr=1-100, for the bacterium, tip and tip path in Fig. 2. (b) Capacitance values at y=0 nm as a function of the relative electric permittivity in log-linear representation. For εr <10 the capacitance values follow a logarithmic dependence which saturates to a nearly constant value for larger values. S2
S2. Bacterium geometry effects on the capacitance signal. Figure S2. (a) Electric potential distribution for the case of a hemiellipsoidal oblate bacterium geometry. The bacterium dimensions are w=1104 nm, h=300 nm and l=2118 nm. The hemiellipsoid bacterium dimensions have been chosen so that the convoluted topographic profile is identical to the one for the full ellipsoid bacterium in Fig. 2 (b) Tip path corresponding to the convoluted hemiellipsoidal bacterium cross-section for a tip of radius R=250 nm at a lift distance zlift=10 nm (green symbols). The grey dashed line represents the hemiellipsoidal bacterium crosssection, while the dark dashed lines the full ellipsoidal bacterium in Fig. 2. (c) Numerically calculated capacitance (red symbols), capacitance cross-talk (black symbols) and intrinsic capacitance (blue symbols) contrast profiles. For comparison, the corresponding values for the full ellipsoid geometry in Fig. 2h are represented as empty symbols. The two geometries provide almost identical results, with only some small differences around the edges of the bacterium. S3
S3. Validation of the methodology with a SiO2 test sample S4
Figure S3. (a)-(d) Topographic, total capacitance, cross-talk capacitance and intrinsic capacitance images for a SiO2 film 235 nm thick and 10 µm wide. Scale bar: 3.7 µm. The cross-talk contribution has been calculated with the help of the capacitance approach curve on the substrate in (e) and the topographic profile along the line in (a) shown in the inset of (e). (f) Total, crosstalk and intrinsic capacitance profiles taken along the lines in (b)-(d). (g) Numerically calculated intrinsic capacitance profiles (dashed lines) for different relative electric permittivities of the silicon dioxide, compared with the experimental profile (thick solid line). Calibrated tip radius R=217 nm, cone angle θ=10º and lift distance zlift=20nm. The comparison gives εr=4-5. (h) Capacitance approach curve measured on the center of the SiO2 (thick solid line) and comparison with theoretically calculated curves (symbols) for different values of the relative electric permittivity. The thin red line is a least square fitting of the theoretical curve to the experimental data, giving εr=4.5±0.5. Inset: approach curve on the bare part of the silicon substrate used to calibrate the tip geometry, with the stray contribution subtracted. S5
S4. Topography de-convolution We report here the procedure of tip de-convolution for an ellipsoid object. The tip apex is represented by a circle of radius R, and the bacterial cell by an ellipse of semiaxes alternatively a=h/2 and b=w/2 or a=h/2, and c=l/2, for the transversal and longitudinals directions, respectively, where h, w and l are the height, width and length of the bacterial cell. For given geometries of the tip and the bacterial cell, it is first found the tangent point between circle and ellipse when both lie on the same ground line (substrate). Then, the parameter n in the superellipse of Eq. (1) is varied until this passes through three points: the center of the circle passing through the tangent point, the center of a circle on top of a bacterial cell, and the center of the circle at one side of the bacterial cell. This superellipse gives the trajectory of the center of the tip apex when a topographic image is recorded in contact with the bacterial cell. Next, the superellipse is translated downwards a distance R+zlift. This gives the movement of the closest point between apex and bacterial cell, in the direction perpendicular to the substrate, when the tip is scanned at distance zlift from the bacterial cell, and it is therefore a convoluted profile. The de-convoluted dimension of a topographic measurement is then obtained by varying the width (or the length) of the bacterial cell until the convoluted profile matches the profile measured from the topographic image. The height is kept fixed to the measured height, since it is not affected by the tip convolution. Figure S4 shows the application of this procedure to two bacterial cells, one measured in dry conditions (a) and one in humid conditions (b). The recovered bacterial cell dimensions obtained from the de-convolution process are listed in Table S1. As it can be seen, bacterial cells kept their volume quite constant (variation below 12%) when changing the atmospheric humidity conditions. S6
Figure S4. (a) Bacterial cell topographic image in dry conditions. (b) Longitudinal (red symbols) and transversal (green symbols) profiles. The continuous lines in (b) represent the fitted convoluted profile according to Eq. (1), and the dashed line the actual bacteria geometry. Data extracted for the present cases: h = 290 nm, w = 963 nm (nw = 2.2), l = 2350 nm (nl = 2.63). The calibrated tip radius was R= 446 nm. (c) and (d) idem for the same bacterial cell in humid conditions. Data extracted: h=300 nm, w = 950 nm (nw = 2.18), l = 2350 nm (nl = 2.63). Calibrated tip radius R = 564 nm. Scale bars 1 µm. Bacterial cell R [nm] h [nm] w [µm] Dry nw l [µm] nl R [nm] h [nm] Humid w [µm] nw l [µm] nl 1 290 0.96 2.20 2.35 2.63 300 0.95 2.18 2.35 2.63 2 446 294 1.08 2.24 1.45 2.38 564 310 0.95 2.18 1.37 2.32 Table S1. Results of tip de-convolution for the two bacteria analyzed. S7
S5. SMM conductance images Figures S5a and S5d show the bacteria SMM conductance images recorded simultaneously to the topographic and SMM capacitance images for the case of dry and humid conditions, respectively. Figures S5b and S5e show the corresponding cross-sectional profiles along the lines in the images. The small contrasts observed in the conductance images are due to some conductance obtained when the tip interacts with the substrate (see Figs. S5c and S5f), and it is not related to a conductance response of the bacterial cell. Most likely this conductance response can be associated to some small residuals remaining from the nanoscale calibration process of the SMM, as we have discussed earlier in Ref. [42]. Figure S5. SMM conductance images obtained on single bacterial cells in (a) dry and (d) humid environments, respectively. Insets: bacterial cell topographic images recorded simultaneously. (b) and (e) corresponding transversal cross-section profiles. (c) and (f) SMM conductance approach curves measured on the metallic substrate (black lines) and on the center of the bacterial cell (red lines), for dry and humid environments, respectively. S8
S6. Relative electric permittivity quantification from single point SMM capacitance approach curves We have also quantified the local electric permittivity of the bacterial cell from single point approach curves, taken on the same bacterial cells analyzed in the paper, in dry and humid conditions. We followed a method similar to those developed for low frequency nanoscale capacitance microscopy 33,36,37 and electrostatic force microscopy. 38-40 The sequence of measurements was the following: first, two approach curves were taken on the metallic substrate (curves 1-2 in Table S2). Next, three approach curves were taken at the top centre of the first bacterial cell (curves 1-2-3 for bacterial cell 1 in Table S3). Then, two more approaches curves where taken on the substrate (curves 3-4 in Table S2) and three more on top of the second bacterial cell (curves 1-2-3 for bacterial cell 2 in Table S3). At the end, two last curves were taken on the metallic substrate, and an image of the bacterial cell was acquired in intermittent contact mode, to verify tip and bacterial cell integrity during the measurements, and used to quantify the intrinsic capacitance. For the radius calibration, we fitted each SMM capacitance approach curve on the metallic substrate with the theoretical capacitance approach curves obtained from the 3D numerical calculations. The fitting parameters are R and kstray, as detailed in the Materials and Methods section. Then, we set as tip radius the average of the values obtained from each couple of curves. Similarly, for the extraction of the relative electric permittivity, each of the three capacitance approach curves on the bacterial cells was fitted with theoretical capacitance approach curves obtained with the 3D numerical calculations. In this case the simulations included the apex geometry (the averaged radii) and the bacteria dimensions resulting from the tip de-convolution, S9
with εr and kstray being the fitting parameters. Examples of the quality of the fittings are shown in Fig. S6. The complete list of results obtained are shown in Table S2 and Table S3. Figure S6. Dielectric constant extraction of a bacterial cell from SMM single point capacitance approach curves in (a) dry and (b) humid conditions. (a) Inset: Experimental (black line) and theoretical (orange line) capacitance single approach curve on the metallic substrate used for tip radius calibration, giving in this case R = 532±9 nm kstray = 213.4±0.8 zf/nm. Main image: Experimental (black line) and theoretical (symbol) single capacitance approach curves on the bacterial cell. A least square fitting (red curve) gives εr = 4.6±0.3 and kstray = 201.2±0.3 zf/nm. Parameters of the simulations: = 531nm, cone angle θ =10º, cone height H =80 µm, cantilever width L = 0 nm, cantilever thickness W = 3 µm. Bacterial cell dimensions: w = 963 nm, l = 2350 nm, h = 290 nm. For humid bacterial cell (b), we obtain, R = 622±5nm, kstray = 215.2±0.4 zf/nm for the single curve on metal, and εr = 21±4 and kstray = 216.1±0.2 zf/nm. Parameters of the S10
simulations: = 631nm, w = 950 nm, l = 2350 nm, h = 300 nm (remaining parameters same as in dry). Curve Dry Humid R [nm] R [nm] kstray[zf/nm] R [nm] R [nm] kstray[zf/nm] 1 529±10 213.3±0.9 640±7 212.7±0.5 2 532±9 531 213.4±0.8 622±5 631 215.2±0.4 MEASUREMENTS ON BACTERIAL CELL 1 3 547±8 207.3±0.6 697±8 205.7±0.6 4 552±6 550 206.1±0.4 623±6 623 215.5±0.4 MEASUREMENTS ON BACTERIAL CELL 2 5 483±7 207.9±0.4 593±6 217.7±0.3 6 410±5 446 215.8±0.3 538±10 564 225.5±0.9 IMAGES Table S2. Results of tip radius calibration. Dry Humid Bacterial cell Curve R [nm] εr kstray[zf/nm] R [nm] εr kstray[zf/nm] 1 4.7±0.8 204.4±0.3 21.4±3.6 216.1±0.2 1 2 531 4.6±0.3 201.2±0.3 631 14.1±1.4 212.5±0.4 3 4.4±0.3 205.6±0.3 9.6±1.6 214.2±0.2 1 3.6±0.3 188.8±0.3 32.2±8.1 220.1±0.1 2 2 550 4.7±0.3 199.0±0.3 623 8.1±0.8 220.4±0.3 3 3.2±0.3 208.4±0.4 29.4±4.3 221.8±0.2 Table S3. Results of relative permittivity extraction. S11
The reproducibility of the results is illustrated in Fig. S4 where we compare the relative electric permittivities obtained from the different measurements. According to these results the overall averaged relative electric permittivities are εr = 4.2±0.6 and εr = 19±10 in dry and humid conditions, respectively. These results are fully compatible with the ones obtained from the image analysis proposed in the main text. We note that the larger variability observed in the data for humid measurements most probably reflect an intrinsic variability of the interaction of the measuring tip with the sample, when moisture is present in the cell wall, similarly to what we observed for low frequency measurements in Ref. [32]. Figure S7. Graphical representation of three independent measurements performed in two different bacteria in dry (RH 5%) and ambient conditions (RH = 40%). The average relative electric permittivity are εr = 4.2±0.6 and εr = 19±10 in dry and humid conditions, respectively. S12