SUPPLEMENTARY INFORMATION

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1 SUPPLEMENTARY INFORMATION DOI: 0.038/NNANO.0.86 Raman, Trigueros et al Mapping nanomechanical properties of live cells using multi-harmonic atomic force microscopy A.Raman, S. Trigueros A. Cartagena, A.P. Z. Stevenson, M. Susilo, E. Nauman, and S. Antoranz Contera In this supplementary material we provide many details to support the main text. In particular, we described in the following sections: A. Speed and spatial resolution of the proposed method B. Near-surface hydrodynamic corrections C. Physics of 0 th harmonic image formation D. Extraction of local material properties from 0 th, st, and nd harmonic observables E. Comparison of mechanical properties of cells extracted using quasi-static curves and the multi-harmonic method F. Additional images G. Additional data on red blood cells sample preparation A. Speed and spatial resolution of the proposed method Table in the main text clearly shows that imaging throughput of our proposed method in mapping local mechanical properties of cells represents ~0-000 times improvement in imaging throughput compared to the standard force-volume method. The high resolution of the method can also be seen by examining the details of, say, the A 0 map on the rat tail fibroblast in Fig S (60 by 60 micron size) taken with 56 by 56 pixels in ~5 minutes. Even at such a large scan size, many cytoskeletal details are clearly distinguished. As another example in Fig. S we show two different live fibroblast cells captured in a 60 micron by 60 micron image (56 by 56 pixels) which clearly resolve cytoskeletal details such as actin bundles in the A 0 maps. NATURE NANOTECHNOLOGY

2 B. Near-surface hydrodynamic corrections Before proceeding to the theory of physics of image formation and the extraction of local properties using the multi-harmonic variables, it is important to highlight an experimental observation using the cantilevers described in the methods section. Conventional theory generally assumes that once the cantilever has been tuned to resonance far from the sample with amplitude π Afar and phase lag φ far = then the cantilever oscillation amplitude and phase change only due to tip-sample interaction forces. In reality for many cantilevers, especially those with short tips such as SiN probes, the hydrodynamic loading changes both the natural frequency and the damping of the cantilever as it comes closer to the sample S. As a consequence the theories of image formation and material property reconstruction require two important considerations. First they needs to account for the difference (often significant) due to viscous hydrodynamics, in the resonant response of the cantilever when located far and the sample. Secondly, the dynamics of the oscillating cantilever interacting with the sample surface needs to be studied. Far from the sample, the natural frequency and quality factor of the fundamental eigenmode of the cantilever can be easily measured using a thermal tune in commercial AFM systems, and are denoted as ω and respectively. The magnetic excitation at far Q far a frequency ω dr must be tuned to exact resonance with ω dr ω far = with a steady state amplitude A far so that the tip motion q ( t) in the driven eigenmode, the phase lag of tip far Supplementary section page

3 oscillation relative to drive φ far, and the magnitude of the magnetic driving force F mag are given by: π q t A F () = sin( ω t φ far far far dr far ), φ far =, mag = (S) Qfar ka where k is the equivalent stiffness of the first eigenmode for which standard calibration methods exist. When this resonant cantilever is brought within imaging distance (when the tip is located <50 nm from surface) to the sample it is well known that the natural frequency and Q-factor decrease significantly to ω < ωdr and Q respectively due to hydrodynamic squeeze film that develops S between the cantilever and the sample surface. As a consequence of this important effect, the amplitude and phase of tip motion change and the tip motion just before engaging the sample now becomes q ( t) = A sin( ωdr t φ ) (S) with A π < A far and φ >. ω and Q can be measured by measuring the thermal spectrum after withdrawing the cantilever from the sample by a small distance (<50nm). Alternately, ω and can also be estimated by knowledge of the Q observables π ωfar, Qfar, Afar, φ far =, A, φ using the forced steady state response of an oscillator as follows. When the sample, we have the following relations from simple forced vibration steady state response theory Supplementary section page 3

4 ka F F mag = ; tan( ) = ω ω dr dr ω dr ka ωdr Q ω + ω Q ω ω far mag = ; φ far = π / (S3) Qfar φ where F mag is the magnitude of the magnetic excitation force. Using (S3) it can be easily shown that the readily observable quantities A, φ are related to ω and as Q follows: ω A φ F φ ω A F sin( φ ) Q A Q ka sin( φ ) dr far mag = cos( ) = cos( ) ω AQfar ka dr far mag = = ω far. (S4) The key point is that both the amplitude and phase of the cantilever change as it is brought from far to within imaging distance of the sample, however this change is due to viscous hydrodynamic effects and must be separated systematically from the amplitude and phase changes that occur due to tip-sample interactions which are discussed now. Consider the equation governing tip motion qt () when it interacts with the sample: q Fmag sin( ωdrt) + Fts( Z + q, q ) + q+ q = ω ωq k F ( Z + q, q ) = F ( Z + q) + F ( Z + q, q ) ts ts, CONS ts, DISS (S5) Supplementary section page 4

5 F ts is the tip sample-interaction force which is assumed to decompose additively into a conservative (tip-sample position dependent) F ts, CONS and a dissipative (tip velocity dependent) component F. F is the magnitude of the magnetic excitation force as ts, DISS mag derived in Eq. (S). Z is the difference between cantilever position and the sample, also known as the Z-piezo displacement (See Fig. S3). Let the steady state motion of the tip interacting with the sample comprise of only the 0 th, st and nd harmonics so that the tip displacement and velocity are qt ( ) = qt ( ) = A0 + Asin( ωdrt φ) + Asin( ωdrt φ) = A0 + Asin( θ) + Asin(θ + φ φ) qt ( ) = Aω cos( θ) + Aω cos(θ + φ φ ) dr dr assuming that these are the dominant harmonics that govern the motion, a fact that is readily observable from experiments in liquids. (S6) In order to calculate the 0 th, st and nd Fourier components of in Eq. (S5) we proceed as follows. Rewriting the interaction force as the sum of purely conservative and non-conservative (in other words dissipative) tip-sample forces, and substituting into it the assumed harmonic motion Eq. (S6) we find: F ts F ( Z + q, q ) = F + F cos( θ ) + F sin( θ) + F cos( θ) + F sin( θ ) (S7) 0 ts ts, CONS ts, DISS ts, CONS ts, CONS ts, DISS In the intermittent contact regime and while oscillating in permanent contact, it can be shown that Fts, CONS( θ ) is symmetric about θ = 3 π /while Fts, DISS( θ ) is antisymmetric about θ = 3 π /. As a result while is the st Fourier sine coefficient, the F F ts, CONS ts, CONS Supplementary section page 5

6 on the other hand is the nd cosine coefficient since sin( θ ) and cos( θ ) are both symmetric about θ = 3 π /. Substituting Eqs. (S6, S7) into (S5a) and balancing separately the constant, and the sine and cosine harmonic terms in the equation, readily leads to the following results that link the Fourier components of the interaction forces to the observables (cantilever amplitudes, phase etc). The i th Fourier coefficient of the conservative interaction force is called the i th harmonic virial and the i th Fourier coefficient of the dissipative interaction force is called the i th harmonic dissipation: ( a) = ka 0 ts, CONS 0 ( b) ω dr Fts, CONS = Fmag cos( φ) + ka ω ( c) ωdr Fts, DISS = Fmag sin( φ) + ka ω Q 4ω dr ω dr ( d) Fts, CONS = ka cos( φ φ) s in(φ φ) ω ωq ( e) F F ts, DISS 4ω dr ω dr = ka sin(φ φ) cos( + φ φ) ω ωq (S8) Eliminating φ among Eqs.(S8b,c) we reach the classical amplitude reduction equation of amplitude modulated-afm: ω ka Fmag / k A =, tan( φ ) = ka dr ω dr ω ω dr F ωeff + Q ωn ear ω ωqeff ω eff F F = ; = ka ω Q ω Q ka ts, CONS ωdr ωdr ts, DISS eff dr Fts, CONS ω ts, DISS (S9) Supplementary section page 6

7 where ωeff is the non-dimensional natural frequency of the cantilever modified by conservative tip-sample interactions and Q eff is the effective Q-factor of the cantilever modified by dissipative tip-sample interactions. Thus amplitude reduction occurs due to both conservative and dissipative tip-sample interactions while the phase reflects the ratio of conservative and dissipative interactions. Recall that when triangular cantilevers with short tips are used, the -surface hydrodynamic effects imply that ω < ω far and Q < Qfar so that A < A far and φ > φ = π. Eq. (S4) connects the quantities ω, far / Q to the observables A, φ. Utilizing Eqs. (S3, 4) in Eq. (S8) we get the following expressions for the 0 th, st and nd harmonics virials and dissipation in terms of the observables: ( a) F = ka 0 ts, CONS 0 ( b) ka far A Fts, CONS = cos( φ) + cos( φ ) Qfar A ( c) ka far A Fts, DISS = sin( φ) + sin( φ ) Qfar A 4A A ( d) Fts, CONS = ka cos( φ φ) cos( φ ) 3 sin( φ A A )sin( φ φ ) 4A A ( e) Fts, DISS = ka sin( φ φ) cos( φ ) 3 + sin( φ )cos( φ φ) A A (S0) C. Physics of 0 th harmonic image formation The 0 th harmonic refers to the DC signal of the of the vibrating cantilever generated due to cycle averaged tip-sample interaction forces which is, in general, different from the deflection curve for an unexcited cantilever in a quasi-static force Supplementary section page 7

8 distance curve. For instance, a strong A 0 signal is created in liquid in a high concentration buffer (so that long range electrostatic forces are screened) when the excited cantilever placed a certain height above the sample intermittently taps on the sample while the same cantilever at the same height from the sample but not vibrating would not deflect appreciably. Once the cantilever is firmly pushed into permanent contact with the sample and if the vibration amplitudes are small compared to the indentation (as in the case of soft live cells) then the 0 th harmonic of the vibrating cantilever equal the static bending of the unexcited cantilever at the same position. However this equivalence is generally not true. Broadly speaking, the generation of the 0 th harmonic is a direct result of nonliity of interaction. There are many fields in physics where the AC excitation of a nonli system generates a 0 th harmonic (thermal expansion, acoustic streaming) as well as a nd harmonic. From Eqs. (S9) and (S8a), the physics of image formation in the topography and 0 th harmonic channels becomes clear. In amplitude modulated AFM, since the amplitude A is regulated by changing Z, a topography image of a live cell in tapping mode in liquids consists of those values of Z that render a constant amplitude A over the scan area, reflecting the combination of tip-sample conservative and dissipative interactions that reduce the amplitude. However since a live cell is so much softer than the microcantilever, the Z-piezo actuator has to push down significantly on a cell to reduce its amplitude to the setpoint amplitude. Thus the topography image of a live cell in liquids using amplitude modulated AFM is not its real topography, and the perceived cell height is significantly reduced since the Z-piezo has to push the cantilever into the cell significantly to reduce the amplitude A to the setpoint value. Thus the material Supplementary section page 8

9 contrast channels such as A0 and φ are not taken at a constant (or approximately) cantilever height Z over the sample, as is the case with stiff or moderately stiff samples (modulus>0mpa). So while on moderately or very stiff materials (glass, mica, purple membrane) in liquids where the measured topography is close to the real one, the 0 th harmonic measures local conservative interactions, on very soft materials such as live cells, the dominant contribution to the 0 th harmonic map arises from the fact that the measured topography itself depends strongly on local conservative and dissipative properties, and this effect dominates the 0 th harmonic map. As a consequence for soft materials such as live cells (modulus -000kPa), the best interpretation of the 0 th harmonic maps is simply that it is a measure of the average force needed to be applied to the cantilever in order to reduce its amplitude to the setpoint amplitude. To understand this better we have performed simulations of AFM microcantilever dynamics on cells in liquids. We have used VEDA.0 - the virtual environment for dynamic AFM, developed by the lead author s group and available online on These simulation tools have been validated against experimental data for tip simulations in liquid environments as described on the manual available online. The simulations use single or multi-mode (or degree of freedom) cantilever models with correct effective stiffness and mass parameters and, and use experimentally measured Q-factors to account for hydrodynamics. In particular we have used the following simulation parameters for a single mode cantilever model for a magnetically excited Olympus TR400 cantilever with SiN tip: k = 0.08 N / m, A = 5nm, A / A = 95%, ω = ω = π(8000) rad / s, Q =.7 sp far far dr far far R = 0 nm, E = 60 GPa, ν = 0.5, ν = 0.3 tip tip tip sample Supplementary section page 9

10 where E tip and ν tip, ν sample are respectively the elastic modulus of the tip and Poisson s ratio of the tip and the sample. The tip-sample interaction model is Hertz contact with Kelvin-Voigt viscoelastic dissipation, so that the sample properties are represented by E sample (kpa) and the sample viscosity by the viscosity parameter μ sample (Pa-s). In these simulations, we varied E sample from 50kPa to 500 MPa, and μ sample from 0.00 Pa-s to Pa-s, and calculate the mean deflection A 0 at the Z distances where the amplitude reduces to the 95% amplitude set point. The results are shown in Fig. S4. Fig. S4 shows clearly that on harder (E sample >MPa), A 0 is strongly correlated to local sample elasticity or local conservative interactions as the Eq. 8(a) would suggest. However for softer, more viscous samples (E sample <500kPa), A 0 becomes much more sensitive to local dissipative interactions, μ sample. The reason is not that Eq. (S8a) is incorrect; on the contrary the simulations show that Eq. (S6) is an excellent approximation of tip motion. A 0 does measure local conservative interactions; however for soft materials the Z distance at which the setpoint amplitude is achieved does depend on a combination of local viscosity (dissipative properties) and elasticity (conservative properties). As a result for soft materials such as cells in liquids, contrasts in A 0 appear both because the Z height depends strongly on the local viscoelasticity of the cell, and also because the local conservative properties themselves change. Supplementary section page 0

11 D. Extraction of local material properties from 0 th, st, and nd harmonic observables We now present in further detail the propsoed method to quantify the local mechanical properties by combining the 0 th, st and nd harmonic data on live cells. First, let us annotate the dynamic tip indentation into the sample as δ () t = ( Z + q) (S) and the average tip indentation as δ 0 = (Z + A 0 ). (S) Next in recognition of the experimental observation that the tip oscillation is much smaller compared to the net average indentation δ 0 on live cells we describe the interaction forces as a Taylor series in δ δ0 to nd order to be consistent with the nd harmonic description of the tip motion: k F = F ( δ ) + k ( δ δ ) + ( δ δ ) + c δ + O ( δ δ ), δ (S3) 3 ( ) sample 3 ts ts 0 sample 0 0 sample 0 δ δ= δ0 where k (N/m) and c (N-s/m) respectively are the conservative force gradient sample sample (stiffness) and damping at that particular indentation value. k sample, δ k = sample δ δ = δ0 is the nd gradient of the interaction force with respect toδ and is a measure of the nonliity of interaction forces in a cycle of oscillation. k sample ksample,, δ and c sample typically change depending on the mean force 0 F ts applied. This Taylor series expansion Supplementary section page

12 is only valid when the tip oscillation amplitude is small compared to the length scale of the interaction forces, or in this case the mean indentation δ 0. It is interesting to note that the quadratic terms in (S3) do not contain a dissipative term. The reason for this is as follows an interaction force term of the type δ would actually not be a truly dissipative force since it would act opposite the tip velocity δ only for half the oscillation cycle, for the other half of the oscillation cycle it would actually act in the direction of tip velocity δ. The first truly dissipative nonli term in the Taylor series expansion (S3) would be a cubic term and is therefore not included in the present analysis which only includes those nonli terms that influence the 0 th, st, and nd harmonics. Substituting (S6) in (S, S) and substituting the resulting expression in (S3) we evaluate the Fourier coefficients of the interaction force in terms of the local properties: ( a) F = F ( δ ) 0 ts, CONS ts 0 ( b) F = k A ts, CONS sample ( c) F = c ω A ts, DISS sample dr ( d) F = k A sin( φ φ ) c Aω cos(φ φ ) k 4 A ( e) F = k A cos( φ φ ) + c Aω sin(φ φ ) ts, CONS sample sample dr sample, δ ts, DISS sample sample dr (S4) Finally we combine Eqs (S0) and (S4) to yield the expressions that connect the 0 th, st, and nd harmonic observables to the local material properties, and take into account the -surface hydrodynamic corrections required when these data are acquired with triangular cantilevers with short tips in liquids: Supplementary section page

13 ( a) F ( δ ) = ka ts 0 0 ( b) ( c) ( d) ka far A ksamplea = cos( φ) + cos( φ ) Qfar A ka far A csampleωdr A = sin( φ) + sin( φ ) Qfar A ksampleasin( φ φ) csampleaωdr cos( φ φ ) ksample, δ A 4 4A A = ka cos( φ φ) cos( φ ) 3 sin( φ )sin( φ φ) A A ( e) k A cos( φ φ ) + c Aω sin( φ φ ) sample sample dr 4A A = ka sin( φ φ) cos( φ ) 3 + sin( φ )cos(φ A A φ ) (S5) Eqs (S5b) and (S5c) can be used to make maps of k and c, while Eq (S5d) can be used to extract the nd order force gradient (or equivalently the stiffness gradient) sample sample ksample, δ F ts, DISS. Eq. S5e arising from is superfluous since the expansion (S3) did not contain any nonli (quadratic) dissipative term as explained earlier. In the absence of such a term Eq. S4e effectively fixes the phase of the second harmonic φ based on the li stiffness and damping properties of the sample. Thus the observables and can be used to determine the effective F ts, CONS F ts, DISS sample stiffness and damping at a mean indentation, F ts, CONS can be used to determine the nd order conservative force gradient (or stiffness gradient), while the observable 0 F ts, CONS measures the force needed to maintain a constant amplitude reduction due to local stiffness and damping. The fact that at each point on the image we know the mean force applied and can extract the effective sample stiffness and damping allows us to estimate quantitatively the local mechanical properties such as the local elastic modulus Supplementary section page 3

14 so long as an analytical tip-sample interaction model is prescribed. For example, in the case of a Hertz contact model with viscoelasticity: 4 * ( ) 3/, Fts = E R Z q when Z + q <0 3 = 0, otherwise (S6) where E * E E ( ω ) E ( ω ) = = + is the complex effective sample storage loss sample sample dr sample dr i ( νsample ) ( νsample ) ( νsample ) modulus (since the tip elastic modulus (SiN) is 5-6 orders of magnitude larger than that of a live cell and thus can be considered essentially rigid) consisting of a storage and a loss modulus representing the li viscoelasticity of the sample evaluated at an average indentation depth below the cell surface. Using the same small oscillation assumptions as above, we find k c sample sample storage Esample = R( δ 0 ) ( ν ) ω dr sample / loss Esample = R( δ 0 ) ( ν ) sample / (S7) From (S6) and (S7) it is easy to find that: 3 ( ν ) sample 0 δ0 = F storage ts, CONS 4 RE sample storage sample 4 R = ( ν sample ) 3 loss sample 4 R = ( ν sample ) 3 /3 E E /3 Fts, CONS 0 ( ts CONS ) A F, /3 Fts, DISS 0 ( ts CONS ) A F, /3 /3 3/ 3/ (S8) Supplementary section page 4

15 These formulas clearly link the observables in a tapping mode scan, and F 0 ts, CONS F ts, CONS storage loss to quantitative local mechanical properties such as local E and and sample F ts, DISS E sample the mean indentation δ 0 at which these are evaluated in the image. Clearly under the basic assumptions of the theory presented here, the nd order force gradient k is sample, δ E sample E sample storage loss not required to determine and in the simple Hertz contact model. However as other tip-sample models with additional unknown parameters are needed, k can sample, δ provide the necessary additional equation to solve for such a constitutive parameter. So far we have only provided the Hertz contact model as an example, however it should be clear that any contact mechanics model of an indentor on an elastic/viscoelastic medium (such as in the Oliver-Pharr indentation model) can be used since the only requirement for the method is the prescription of local stiffness, stiffness gradient and damping coefficient, in terms of local constitutive properties. In the next section we compare the elastic moduli and local stiffness obtained while using the above multi-harmonic method and from the conventional pointwise force-distance force spectroscopy. E. Comparison of mechanical properties extracted from quasi-static F-Z curves and the multi-harmonic method In order to compare the mechanical properties extracted using the new multiharmonic method with those extracted using conventional F-Z curves, we made a careful comparison of the two methods for fibroblasts and for bacterial cells. F-Z curves during approach and retraction were repeated many times at slow speeds the Supplementary section page 5

16 center of the bacteria or cell at a point indicated by a cross in the Figs. S5 and S6. These data were converted into Force indentation curves and either a li stiffness model or a Hertz contact model with tip radius of 45 nm and sample Poisson s ratio of 0.3 were used to fit the measured curve. The Z position at contact is solved as a part of the fitting process as described earlier in Radmacher et al S. Strictly speaking, the new multi-harmonic method for extracting local elastic properties is so different from the conventional method using F-Z curves that comparing the extracted values using the two methods is not really justifiable. For example in the case of F-Z curves, one matches the entire force-distance curve to a model starting from the first point of contact, while in the new method one tracks the local effective force gradients at a specific mean indentation value which changes from point to point on the image. Secondly the effective properties using the new method correspond to viscoelastic properties measured at much higher frequencies than the conventional F-Z curves which are performed at much smaller frequencies. Because viscoelastic properties of biomaterials are strongly frequency dependent, it is only natural that the values extracted using the new multi-harmonic method be different from those of the quasi-static method. Nonetheless it is instructive to examine these differences for the bacterial and fibroblast samples. In Fig. S5b, for an E. Coli bacterium, the local stiffnesses are typically in the range N/m. These maps reflect the internal turgor pressure in these cells as well as local mechanical properties of the peptidoglycan network S3. The F-Z curves are repeated on the equator of this bacterium (Fig. S5c) and the results are converted to local elastic stiffness, revealing stiffness in the range N/m, ly an order Supplementary section page 6

17 of magnitude softer than those obtained using the multi-harmonic method. This surprising result is resolved by taking into account the strongly viscoelastic response of the bacterial cell wall S4 which stiffen substantial when probed at higher frequencies. In this case the cantilever is driven at ~khz at its resonance. In Fig. S6, we consider data collected using a different set of fibroblast cells than those presented in the main text. These cells were imaged towards the end of the experimental period when many cells die. As can be seen the local elastic modulus maps taken at a drive frequency of ~8kHz show When compared with storage E sample storage E sample values in the range 50-00kPa. values extracted from repeated F-Z curves, we find a value the center of the cell in the range 80-00kPa, which is ly half of what is indicated at the same point on the cell using the new method. In this case the extracted storage E sample value from F-Z curves is itself quite high compared to prior works on fibroblasts (Table S), and by itself is somewhat lower than the value extracted from the new method. That these modulus values are stiffer than those indicated by prior AFM work on fibroblasts can be understood by the fact that the cell properties vary a lot depending on their stage in the life cycle. These cells in particular are older and closer to death since they were imaged towards the end of the storage experimental period. Nonetheless we find consistently that the using the new method typically is larger than that from quasi-static F-Z curves due to the natural frequency dependent viscoelasticity of such samples. E sample Supplementary section page 7

18 Table S. Summary of prior work using different experimental modalities to measure the local elasticity of rat fibroblasts. Experimental Modality Estimated modulus References Rotation of ferromagnetic beads 0. - kpa Eckes et al., 998 S5 bound to cell membrane Quasi-static AFM indentation 3 30 kpa Rotsch, et al., 999 S Thermal excitation of fluorescent kpa Kole et al., 005 S6 microspheres Quasi-static AFM indentation 5-30 kpa Solon et al., 007 S7 Magnetic tweezers -0 kpa Klemm et al. 00 S8 Force Mapping mode -50 kpa Haga et al. 000 S9 It is also instructive to compare the elastic moduli reported on live fibroblasts using AFM and other methods such as torsion of magnetic beads that probe the local membrane properties (Table S). It is clear that methods that locally probe the mechanics of the membrane report much lower elastic moduli than AFM based methods that are based on nanoindentation normal to the surface. This suggests that the cells exhibit fundamentally different material properties across hierarchical length scales. F. Additional Figures In Fig. S7 we provide images taken with TR800 cantilevers in the acoustic mode instead of the magnetically excited levers discussed in the main text, showing that the multi-harmonics can easily be observed using the acoustic mode excitation also. However the conversion of these maps into quantitative maps of local stiffness or damping cannot be achieved since equations (S3, S4) do not hold for acoustically excited cantilevers due to spurious resonances that change the shape (transfer function) of the cantilever resonance S0. Supplementary section page 8

19 In Figs. S8 and S9 we provide further material maps of E. Coli taken with Lorentz force excited TR800 cantilevers to show that the 0 th, st and nd harmonic channels do indeed pick out distinct contrasts in local material properties on E.coli bacteria. First the local material properties (stiffness, damping, nd order force gradients) on these samples are similar to those presented in Fig. in the main text. Moreover one can clearly see the influence of the moving flagella of the bacteria in Fig. S9. In both Figs. S8 and S9 one generally sees material property contrasts far from edges so that tip convolution effects are not likely to play a role in these contrasts. G. Additional data on red blood cells sample preparation The characteristic biconcave morphology of live red blood cells (RBC) is highly sensitive to the imaging buffer used. In this work we conducted AMPLITUDE MODULATED AFM on live cells in phosphate buffered saline (PBS, x), and found RBC to be semi-spherically shaped (Fig. 4 in text). This morphology has previously been reported under similar conditions S, and we confirm this effect by optically imaging fresh RBC in a range of PBS buffer concentrations and in Fetal Bovine Serum (Sigma- Aldrich, Dorset, UK) as a physiological control (Fig. S0). RBC in serum exhibited the expected biconcave shape (a), while cells in PBS 0.5x were swollen (b), due to the hypotonic conditions. Cells in PBS x (c) exhibited a predominantly crenate morphology as a result of hypertonic conditions, however cells with a biconcave morphology can also be observed. PBS 0x (d) induced a higher level of hypertonicity with all cells severely crenate, expected given the much higher salt concentration. Imaging in PBS x therefore precluded the biconcave morphology in the majority of cells. We suggest the Supplementary section page 9

20 morphology observed under AFM is due to the combined effects of buffer hypertonicity and adhesion between RBC and the polylysine surface (e). Supplementary section page 0

21 References for supplementary material [S] X. Xu, C. Carrasco, P. J. de Pablo, J. Gomez-Herrero, A. Raman, Unmasking imaging forces on soft biological samples in liquids: case study on viral capsids, 95, 950, Biophys. J., 008. [S] C. Rotsch, K. Jacobsen, M. Radmacher, Dimensional and mechanical dynamics of active and stable edges in motile fibroblasts investigated by using atomic force microscopy, Proc. Natl. Acad. of Sci., 96(3), 9, 999. [S3] M. Arnoldi, M. Fritz, E. Bäuerlein, M. Radmacher, E. Sackmann, and A. Boulbitch, Bacterial turgor pressure can be measured by atomic force microscopy, Phys. Rev. E, 6(), 034, 000. [S4] V. Vadillo-Rodriguez, J. R. Dutcher, Dynamic viscoelastic behavior of individual gram negative bacterial cells, Soft Matter, 5, 50, 009. [S5] B Eckes, D Dogic, E Colucci-Guyon, N Wang, A Maniotis, D Ingber, A Merckling, F Langa, M Aumailley, A Delouvee, V Koteliansky, C Babinet, and T Krieg, Impaired mechanical stability, migration and contractile capacity in vimentindeficient fibroblasts, J. Cell Sci.,, 897, 998. [S6] T. P. Kole, Y. Tseng, I. Jiang, D. Wirtz, Intracellular mechanics of migrating fibroblasts, Mol. Biol. Cell, 6(), 38, 005. [S7] J. Solon, I. Levental, K. Sengupta, P.C. Georges, P. A., Janmey, Fibroblast adaptation and stiffness matching to soft elastic substrates, Biophys. J., 93(), 4453, 007. Supplementary section page

22 [S8] A. H. Klemm, S. Kienle, J. Rheinlander, T. E. Schaffer, W. H. Goldmann, The influence of Pyk on the mechanical properties in fibroblasts, Biochemical and Biophys. Res. Comm., 393 (4), 694, 00. [S9] H. Haga, S. Sasaki, K. Kawabata, E. Ito, T. Ushiki, T. Sambongi, Elasticity mapping of living fibroblast by AFM and immunofluorescence observation of the cytoskeleton, Ultramicroscopy, 8, 53-58, 000. [S0] X.Xu, A. Raman, Comparative dynamics of magnetically, acoustically, and brownian motion excited microcantilevers in liquid atomic force microscopy, J. App. Phys., 0(3), 007. [S] S. Sen, S. Subramanian, D.E. Discher, Indentation and adhesive probing of a cell membrane with AFM: theoretical model and experiments, Biophys. J., 89(5), 303-3, 005. Supplementary section page

23 A 0 A 0 A 0 Figure S: The A 0 map acquired on the rat fibroblast cell of Fig. 3 of the main text shown on a larger scale along with image zoom-ins clearly resolves the actin bundles and cytoskeletal features. Supplementary section page 3

24 Figure S: a, Topography images of two live rat tail fibroblast cells scanned with magnetically excited cantilever (Imaging conditions and parameters k=0.065n/m, w far =7.4kHz, Q far =.7, A far =.5 nm, A =4.5 nm, setpoint ratio: 70%, scan rate: 0.5Hz/ line) show little contrast associated with the cytoskeleton. b, On the other hand A 0 maps acquired simultaneously with the topography show clear contrasts in local material properties associated with the cytoskeleton. c, A zoom in of the material contrast maps clearly show the actin bundles and cytoskeletal features at high resolution. Length scale bar is 0 microns. Supplementary section page 4

25 Figure S3. a, A schematic of an oscillating cantilever showing the key motion/displacement variables. the schematic emphasizes that while operating in liquids it becomes necessary to account for the average deflection of the tip A 0, which is generally comparable to the setpoint amplitude of the drive harmonic A. b, A schematic shows the time history of tip motion (in terms of θ ) to leading order, along with the conservative and non-conservative tip-sample interaction forces encountered by the tip during this motion. Supplementary section page 5

26 Figure S4. a, A graph of A 0 vs sample elastic modulus E sample (kpa) and the sample viscosity μ sample (Pa-s) can be computed for a TR400 cantilever tapping on samples in liquid environments using the Virtual Environment for Dynamic AFM (VEDA.0 on software. b, The same results can be shown as graphs of A 0 vs μ sample (Pa-s) for different E sample values and demonstrate that for moderate to high elastic stiffness samples A 0 generally depends on local conservative (elastic stiffness) properties and is independent of viscosity, but for soft materials A 0 also begins to depend on the local viscosity. Supplementary section page 6

27 Figure S5. a, Topography image of an E. coli cell taken using magnetic (Lorentz force) excitation with a TR800 lever showing a well-defined bacterial cell. b, Image showing the corresponding map of local spring constant of sample derived from the A 0, A, φ maps as described in the text. c, A typical graph of quasi-static Force-Z response on the center of the E. coli cell as shown by the cross in a, d-e, Histograms showing the variations of local spring constant derived from multiple replicates of force-z curves at a point indicated by X in a from both tip approach (or Z piezo extension) and tip retraction data. Supplementary section page 7

28 Figure S6. a, Topography image of a rat fibroblast cell cell taken using magnetic (Lorentz force) excitation with a TR400 lever showing three different cells in buffer solution. b, Image of the local storage modulus of sample derived from the A 0, A, φ maps as described in the text. c, Quasi-static Force-Z curves on the center of a cell as shown by the cross in a. d-e, Histograms showing the variation of the local spring constant derived from multiple replicates of force-z curves at a point indicated by X in a from both tip approach (or Z piezo extension) and tip retraction data. Supplementary section page 8

29 Figure S7. a-e, Images of the topography, φ, A 0, A, and φ of an E. coli cell on polylysine covered mica sample using piezo (acoustic) excitation on a TR800 cantilever clearly show heterogeneities in local mechanical properties. The operating conditions used are described in the methods section of the main text. Supplementary section page 9

30 Figure S8. a, Topography image of an additional live E. coli cell scan using a magnetically excited Olympus TR800 cantilever (see materials and methods) showing a small bacterial cell. b-c, Maps of the multi-harmonic data (A 0, φ ) acquired simultaneously clearly show heterogeneities not captured in the topography. d-f, Maps of mean indentation (nm), local dynamic stiffness (N/m), damping (N-s/m) can be extracted from the multi-harmonic variables using the theory described in the text. g-h, Maps of multi-harmonic data (A, φ ) acquired with the topography show less contrast over the cell surface. i, These multi-harmonic observables are converted to a map of the local nd order force gradient (N/m ) using the theory described in the text. The scale bar represents 500nm, and this is a 56 by 56 pixel image taken in ~5 minutes. Supplementary section page 30

31 Figure S9 a, Topography image of another live E. coli cell scan using a magnetically excited Olympus TR800 cantilever (see materials and methods) showing a well defined bacterial cell with a emergent flagella the top of the cell. b-c, Maps of the multiharmonic data (A 0, φ ) acquired simultaneously clearly show heterogeneities not captured in the topography. d-f, Maps of mean indentation (nm), local dynamic stiffness (N/m), damping (N-s/m) can be extracted from the multi-harmonic variables using the theory described in the text. g-h, Maps of multi-harmonic data (A, φ ) acquired with the topography show less contrast over the cell surface. i, These multi-harmonic observables are converted to a map of the local nd order force gradient (N/m ) using the theory described in the text. The scale bar represents 500nm, and this is a 56 by 56 pixel image taken in ~5 minutes. Supplementary section page 3

32 Figure S0. a, Optical bright field image of red blood cells acquired with 00x oil immersion objective in Fetal Bovine Serum (Sigma-Aldrich, Dorset, UK) show the typical biconcave morphology of the cells. b-d, Dark field images with differential interference contrast (DIC) of the red blood cells in 0.5x PBS, and x PBS, and 0x PBS buffers show a different cell morphologies. e, A model of red blood cell morphology when landing on glass in x PBS solution. Scale bar: 5 μm. Supplementary section page 3