Supplementary Information. Fast, multi-frequency, and quantitative nanomechanical imaging of live cells using the atomic force microscope

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1 Supplementary Information ast multi-frequency and quantitative nanomechanical imaging of live cells using the atomic force microscope lexander X. Cartagena-Rivera ± Wen-Horng Wang 3 Robert L. Geahlen 34 and rvind Raman * School of Mechanical ngineering Purdue University West Lafayette Indiana US Birck Nanotechnology Center Purdue University West Lafayette Indiana US 3 Department of Medicinal Chemistry and Molecular Pharmacology Purdue University West Lafayette Indiana US 4 Purdue University Center for Cancer Research Purdue University West Lafayette Indiana US ±Present adess: Laboratory of Cellular Biology Section on uditory Mechanics National Institute on Deafness and Other Communications Disorders National Institutes of Health Bethesda Maryland US This supplementary documentation has been created to provide additional information to support the main text. The sections discussed in this document are: a. Direct versus other microcantilever excitation methods in tip-surface coupled M in liquids b. Liized spring and dashpot of a two-element Kelvin-Voigt viscoelasticity model c. Viscoelastic Sneddon s contact mechanics model d. Bottom effect cone correction (BCC) of the Sneddon s model with viscoelasticity extension e. Bimodal M imaging for viscoelastic property mapping f. dditional images of nanomechanial properties of rat fibroblast cells g. dhesion experiments h. How well the BCC contact mechanics model fits the experimental data i. Movies of additional MD-MB-3 human breast cancer cell expressing Syk and treated with inhibitor a. Direct versus other microcantilever excitation methods in tip-surface coupled M in liquids Many directly and indirect excitations are commonly used for atomic force microscopy in liquids (-5). However for extracting quantitative information direct excitation is required since it leads to well-defined microcantilever s in liquids. The most frequently used direct excitation methods are magnetic (-) and

2 photothermal (3-4) actuation. Indirect excitations are acoustic () and (5) actuation. Below is a brief description of each excitation method: coustic mode is the most widely used method and consists of a piezoelectric transducer or dither piezo attached to the cantilever holder and vibrated at high frequencies to excite the microcantilever. This excitation method not only ives the cantilever but also the chip holder and surrounding liquid. This generates an effect called forest of peaks that masks out the real microcantilever vibration response. second more difficult effect to understand is that of fluid borne excitation which has a major influence on cantilever s even if the forest of peaks effect is resolved (6). Sample excitation can be done with a piezo-electric transducer located underneath the and vibrated. The microcantilever is then brought into direct physical contact with the vibrating exciting the cantilever. n issue is that this excitation excites the and the liquid creating unwanted resonances that masks out the real microcantilever vibration response. Photothermal excitation uses a high powered laser to excite M microcantilevers in liquids yielding clean/smooth resonant peaks without spurious peaks and with a wide frequency bandwidth. However phototermal efficiency is low requiring large amounts of laser power to mechanically actuate the cantilever a few nanometers resulting in local heat that can potentially damage sensitive s and accelerate liquid evaporation. or direct magnetic excitation as the name implies only the microcantilever is directly excited and a clean vibration response is obtained. There are two ways of doing this: (a) magnetic which consists of a paramagnetic coating on the microcantilever backbone that will be excited by a solenoid such that applying a alternating current to it generates a magnetic field that interacts and excites the coated microcantilever. (b) idrive which is a technology that consists of triangular V-shaped cantilever that is gold coated. n alternating current is applied to the cantilever generating an electric field that will interact with a magnetic field generated by a permanent magnet. This is the so called Lorentz force excitation. Choosing the optimal excitation method for the microcantilever is important for quantitative spectroscopy measurements. We put to test the 3 excitation schemes while in contact with a and determined the ideal for extracting quantitative information. igure S shows the response spectra of a TR4PB cantilever acquired in contact with a glass slide in PBS for the 3 excitation methods. s shown clearly in ig. S the excitation method that yields a smooth transfer function in which changes in amplitude and phase can be easily recorded and used to reconstruct the conservative and dissipative tip- interactions is the directly excited idrive method. Thus we chose

3 this method over the other conventional actuation methods for our quantitative experiments. b. Liized spring and dashpot of a two-element Kelvin-Voigt viscoelasticity model Because we use special soft cantilever with short tips for cell imaging the hyo loading changes both the natural frequency and the damping of the cantilever as it comes closer to the surface [7-8]. s a consequence the theories for nanomechanical properties mapping requires two important considerations: (a) they must account for the difference (often significant) due to viscous hyos in the resonant response of the cantilever when located and the surface and (b) the s of the harmonically oscillating cantilevers interacting with the surface. rom li vibration theory for a point mass oscillator of natural frequency and Q factor Q n excited by a harmonic force: q q q Q mag n n n cant the steady state vibration response is: q( t) sin( t ) k mag cant sin( t) k n Q n n n Qn n Qnn tan n Qnn sin n Qn n cos n. n (S). (S)

4 Using the above it can be easily shown that when the ive frequency is tuned to achieve maximum amplitude the following hold: Q n mag Q k cant 4Q tan 4Q. (S3) We will use these relationships several times in the following derivation. xtracting local cellular mechanical properties: ar from the the natural frequency and Q-factor of the cantilever are Q. The ive excitation frequency is tuned to achieve maximum amplitude. Hence q. S applies and we have the following relationships for the amplitude and phase from the 4Q mag k Q cant (S4) tan 4Q. Note that when tuning the cantilever from the phase lag at the frequency of peak amplitude is not to be set to or 9 rather it should be set to which say for Q is a surprising 75 [9]. tan 4Q When brought the and prior to the tip- interaction the natural frequency and Q-factor of the cantilever change to Q and as a consequence the amplitude and phase also change to. Thus the excitation frequency no longer corresponds to the ive frequency at which maximum amplitude occurs. So we invoke the more general q. S:

5 r r Q r Q sin r r Q r cos. Where k r. mag cant rom qs. (S5a) and (S5c) we get: r r Q (S5) cos kcant mag sin. Q k mag cant Or Q mag cos k cant mag sin mag cos. k k cant cant (S6) But from q. S5a which can be substituted in q. (5) to yield: k cant mag Q 4Q (S6 )

6 4Q cos Q sin. Or cos 4Q Q Q 4Q Q Q cos sin 4Q Q 4 Q Q. (S7) Dynamics while interacting with the Now the equation of motion of the vibrating cantilever interacting with the soft cell becomes: q sin( t) q q Q k mag ts cant whose steady state solution is expected in the form (S8) q( t) sin t (S9) so that the tip indentation into the is: ( t) sin t ccordingly Substituting (S9) and () into (S8): where Z. ( ) k ( ) c ts ts. (S) ( ) k sin( t ) c cos( t ). ts (S)

7 sin t cos( t ) sin t Q mag sin( t ) ts( ) k sin( t ) c cos( t ) kcant (S) and collecting together terms in sin t or both sides of the equation (S) gives us: k ( ) cant ts kcant mag cos k kcant mag sin c. Q q. (S3) can be simplified using qs. (S7) and (S6 ) as thus: ( ) k k ts cant cos t and equating them on k k cos cos Q 4 Q Q cant cant (S3) (S4) k cant kcant c sin sin. Q 4 Q Q These equations apply for both tapping mode observables and also for contact mode (with resonant excitation) observables. c. Viscoelastic Sneddon s contact mechanics model The fact that at each point on the image we can solve for the local force and damping gradients allows the extraction of unknown constitutive material properties which are a more fundamental physical properties of cells by using a tip- contact mechanic model of interest [9-]. The Sneddon s contact mechanics model which is a modification of the standard Hertz contact mechanics model for axisymmetric tips was used with a li viscoelastic expansion []. The viscoelastic Sneddon s model for a cone-shaped M tip used in this study; * ts tan( ) (S5)

8 with ts tip- interaction force (N); * Sneddon Cone( ) Sneddon Cone( ) i the complex effective modulus consisting of an elastic viscous Sneddon Cone and Sneddon Cone modulus representing the li viscoelasticity of the evaluated at an average indentation depth (Pa); half-space cone angle of the cantilever; and mean indentation [-]. Using the small oscillation assumption which means that the M probe oscillation amplitude is much smaller than the average indentation on soft s the tip- interaction force as a Taylor series expression in : k c O (S6) ts ts. Using q. S6 for small oscillations assumptions as above and neglecting the contribution of the higher order terms in Taylor series expansion and in the multiplicative correction we find that: ts k c 4 SneddonCone 4 SneddonCone tan tan. (S7) Now we present in further detail the method to quantify the local mechanical properties by combining the experimental multi-harmonic observables th and st data on live cells let first write the expression of the and average tip indentation t into the as: t Z q Z t sin Z. (S8) where Z is the piezo movement is the cantilever mean deflection is the first harmonic amplitude and is the first harmonic phase lag. Substituting qs. S8 into resulting qs. S6 and S7 we can solve for the unknown constitutive parameters:

9 (S9) tan ts CONS SneddonCone SneddonCone SneddonCone ts CONS 8 tan ts CONS ts DISS 8 tan ts CONS. inally the force harmonics ( th and st ourier components of the tip- interaction force for live cells) of the tip- interaction force in terms of the multiharmonic observables ( and ) were previously derived in (Raman et al. []) and with a slight modification using the hyo correction derived in (Cartagena et al. [9]) for soft and low Q factor microcantilevers tuned to the peak amplitude of the resonance curve from the surface the resulting formulae are: k ts CONS cant k cant cos cos Q 4Q ts CONS k cant sin sin. Q 4Q ts DISS (S) d. Bottom effect cone correction (BCC) of the Sneddon s model with viscoelasticity extension Sneddon s contact mechanics model requires small indentations <% of height. However a model that takes into account the artifact generated by moderate and large indentations of conical tips in M measurements on thin s and adherent cells is required. In this case we chose to use the BCC contact model [3] which is a multiplicative analytical correction done to the commonly used Sneddon s model. This is a non-artifactual contact mechanics model that takes into consideration topographical effects by large indentations in soft s like live cells. or a cell thickness of ~4 µm as used in this work an indentation of larger than 4-8 nm would be needed to violate the assumptions of the standard Sneddon s model. However all the measurements made here have been for indentations less than 4 nm. Because as shown before [9-] cantilever oscillation amplitude is small compared to indentations it is reasonable to use a li viscoelastic model to extract the

10 constitutive material properties like elastic and viscous modulus. Thus the resulting tip- interaction force model is: * 3 8 tan tan ts tan O when 3 3 h h h otherwise where (S) * BCC ( ) BCC ( ) i is the complex effective modulus consisting of an elastic BCC and viscous BCC modulus representing the li viscoelasticity of the evaluated at an average indentation depth. h and respectively are the indentation the height of the at that location and the half-opening angle of the cone. Using q. S6 for small oscillations assumptions as previously presented and neglecting the contribution of the higher order terms in ts Taylor series expansion and in the multiplicative correction we find that: k c 8BCC tan tan tan 3 h h (S) 8BCC tan tan tan. 3 h h Substituting qs. S8 into resulting qs. S6 and S and evaluating the ourier coefficients of the tip- interaction force are: 8BCC tan tan tan 3 h h ts CONS 8BCC tan tan tan 3 h h ts CONS ts DISS 8BCC tan tan tan. 3 h h (S3)

11 where is the th ourier coefficient of the conservative interaction force ts CONS ts CONS is the st ourier coefficient of the conservative interaction force and is the st ourier coefficient of the dissipative interaction force (q. S). ts DISS Defining dimensionless parameter and rearranging the equations: h h (average indentation against topography) tan h ( h) tan tanh tan h h ts CONS ts CONSh 8BCC tan h tan h tan h 3 ts CONS h 8 tan tan tan ts CONS BCC h h h h 3 8BCC tan h tan h tan h. 3 ts DISS h (S4) These expressions clearly link the experimental observables to quantitatively extract the nanoscale constitutive mechanical properties BCC and BCC. MTLB code has been written that performs a nonli least squares best fit of those unknown nanomechanical properties BCC and BCC that best match the measured force harmonics formulas qs. S4 and S [9-]. It is important to keep in mind that these equations actually extract the effective properties of the live cell at a specific mean indentation and excitation frequency [9]. With the above briefly discussed theory and the maps of multi-harmonic amplitudes and phases ( and ) that can be easily acquired on a live cancer cell in vitro it's possible to map the mean indentation ( ) and the complex elastic modulus of the viscoelastic ( e. Bimodal M imaging for viscoelastic property mapping BCC and BCC ). or bimodal experiments because of the cell softness and the low Q-factor of the soft cantilever in liquids the vibrational mode shapes of the cantilever are assumed to be unperturbed. Moreover since the cantilever oscillations are much smaller than the net indentation into the cell it can be assumed that the equation-of-motion of the cantilever can be separated into two independent simple harmonic oscillators [4]. Therefore we

12 can model the governing s of the soft cantilever in permanent contact on the cell surface in liquid as: q q mag sin( t) ts q Q k q cant q sin( t) q Q k mag ts cant (S5) where q is the contribution to tip deflection of st eigenmode q is the contribution to tip deflection of nd eigenmode is the resonance frequency of st eigenmode is the resonance frequency of nd eigenmode Q is the quality factor of st eigenmode Q is quality factor of nd eigenmode kcantis the effective spring constant of st eigenmode and kcant is the effective spring constant of nd eigenmode respectively. The constitutive unknown parameters are solved by combining the reconstructed tip- interaction force and the Sneddon s contact mechanics model. ollowing the derivation of Supplementary Information Section c the resulting analytical equations to solve for the unknown constitutive parameters stiffness k k and c c are:

13 tan ts CONS SneddonCone SneddonCone SneddonCone and ts CONS 8 tan ts CONS ts DISS 8 tan ts CONS ts CONS Sneddon Cone tan SneddonCone SneddonCone ts CONS 8 tan ts CONS ts DISS 8 tan ts CONS. (S6) f. dditional images of nanomechanical properties of rat fibroblast cells In this work we performed multiple fast M imaging of live rat fibroblasts and MD- MB-3 human breast cancer cells using Lorentz-force microcantilever excitation with feedback on the cantilever mean deflection. fter imaging we extracted their nanomechanical properties. In ig S3 we provide additional images of a living fibroblast cell in culture media showing that this novel technique can be easily implemented with repeatability and confidence yielding reasonable quantitative nanomechanical values. igure S4 shows the viscoelastic tangent tan maps obtained at two widely spaced high frequencies (7 khz and 6 khz) on a live rat fibroblast cell in culture media. tan maps igs. S4(a and b) clearly shows the classical viscoelastic frequency dependence. igure S4c is the difference between the low and high frequency tan maps showing a reduction by ~.3-.9 on the cell. g. dhesion experiments The expression in MD-MB-3 cells of Syk decreases cell motility and enhances adhesion. To confirm that this effect is an intrinsic property of the active kinase we compared cells either lacking Syk or expressing Syk-GP (wild-type Syk with a green fluorescent protein tag) or Syk-QL-GP an analog-sensitive version of Syk. The treatment with -NM-PP an orthogonal inhibitor of Syk-QL-GP of cells expressing

14 the engineered kinase but not the wild-type enzyme reduced adhesion to the level seen with Syk-deficient cells (ig. S5). These experiments illustrate the ability of Syk to enhance cell adhesion in a manner dependent on its catalytic activity. h. How well the BCC contact mechanics model fits the experimental data We used a nonli least-squared fit algorithm to best fit the unknown physical properties to the experimental data M observables. In order to check the applicability of the contact model and the experimental data we extracted the residuals and resnorm of the fit. The residuals measure the differences between a data point and the corresponding mechanics models estimate therefore the smaller the difference the better the fit. However residuals can be positive or negative making it difficult sometimes to judge if the fit is good. The resnorm is a better estimate consisting in the sum of squared residuals. igure S6 show the extracted values for the residuals and resnorm are very small confirming the goodness of the fit. i. Movies of additional MD-MB-3 human breast cancer cell expressing Syk and treated with inhibitor We present an additional example of the MD-MB-3 human breast cancer cells expressing Syk-QL-GP after addition of -NMPP for Syk inhibition. Movies S-S3 show the time-varying changes in the multi-harmonic observables signals. Movies S4- S6 show the extracted nanomechanical properties presenting progressive changes in the elastic and viscous and the indentation. The movies have a total of 4 images. ach image was obtained at min 3 s intervals with a total time of mins. The movies provide insights into the kinetics of cytoskeletal changes. Interestingly rapid changes in the cytoskeletal architecture at the cell periphery could be visualized within.5 min including the formation and movement of lateral actin bands or transverse arcs characteristic of retrograde actin flow that preceded the release of focal adhesions. Thus the rapid of Syk activity was correlated with amatic rearrangements in the cortical actin cytoskeleton.

15 References. Xu X. & Raman. Comparative s of magnetically acoustically and Brownian motion iven microcantilevers in liquids. J. ppl. Phys (7).. nders O. Korte. & Kolb H.. Lorentz-force-induced excitation of cantilevers for oscillation-mode scanning probe microscopy. Surf. Interface nal (4). 3. Kiracofe D. Kobayashi K. Labuda. Raman. & Yamada H. High efficiency laser photothermal excitation of microcantilever vibrations in air and liquids. Rev. Sci. Instrum (). 4. Labuda. et al. Comparison of photothermal and piezoacoustic excitation methods for frequency and phase modulation atomic force microscopy in liquid environments. IP dvances 36 (). 5. Rabe U. & rnold W. coustic microscopy by atomic force microscopy. ppl. Phys. Lett (994). 6. Kiracofe D. & Raman. Quantitative force and dissipation measurements in liquids using piezo-excited atomic force microscopy: a unifying theory. Nanotechnology 4855 (). 7. Tung R. C. Jana. & Raman. Hyo loading of microcantilevers oscillating rigid walls. J. ppl. Phys (8). 8. Xu X. Carrasco C. de Pablo P. J. Gomez-Herrero J. & Raman. Unmasking imaging forces on soft biological s in liquids when using atomic force microscopy: a case study on viral capsids. Biophys. J (8). 9. Cartagena. & Raman. Local viscoelastic properties of live cells investigated using and quasi-static atomic force microscopy methods. Biophys. J (4).. Raman. et al. Mapping nanomechanical properties of live cells using multiharmonic atomic force microscopy. Nature Nanotech ().. Sneddon I.N. (965) The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary profile. Int. J. ngng. Sci lcaraz J. Buscemi L. Grabulosa M. Trepat X. abry B. arré R. and Navajas D. (3) Microrheology of human lung epithelial cells measured by atomic force microscopy. Biophys. J Gavara N. & Chadwick R. S. Determination of the elastic moduli of thin s and adherent cells using conical atomic force microscope tips. Nature Nanotech (). 4. Xu X. Melcher J. & Raman. ccurate force spectroscopy in tapping mode atomic force microscopy in liquids. Phys. Rev. B ().

16 Supplementary igures igure S. Using different excitation techniques for tip-surface coupled M probes in liquids. Tune curves (a) amplitude (nm) and (b) phase lag (deg) performed using different cantilever excitation methods on a glass surface: acoustic (red) (green) and idrive-magnetic (blue). IDrive is the only excitation method that retains the transfer function of a single harmonic oscillator. This clearly shows that magnetic excitation is the natural choice for quantitative measurements in liquids.

17 igure S. dditional nanomechanical images of live rat fibroblast cells. (a) Topography image of a live rat fibroblast cell scanned in physiological media solution using Lorentz excited cantilever with regulation (see Materials and Methods). (b-d) Multi-harmonic images of ( ) acquired simultaneously with topography showing high resolution subcellular contrast related to the local physical properties. (f-g) Maps of local stiffness k and damping c extracted from the multiharmonic data and using the li model described in the Supplementary Information. (h-j) Maps of local modulus local modulus and mean indentation extracted using the multi-harmonic data and the BCC contact mechanics model described in the Supplementary Information B. Imaging parameters; f =7.9 khz k cant =87.4 pn/nm Q =.75 =35 and sp =5 nm. The scale bar on images represents 8 μm (size; 4x4 μm pixels; 56x56 acquisition time; 3 min 3s).

18 igure S3. dditional rat fibroblast cell using new technique with bimodal. Multifrequency observables images (a) DC signal mean deflection first and second flexural eigenmodes amplitudes and phases (b-c) and (d-e) obtained simultaneously using the previously described M method. (f-g) Maps of local stiffness k (N m - ) and damping c (N s m - ) extracted from the measured first mode data ( f =7.6 khz) using the theory described in the text and Supplementary Information. (h-i) Maps of local stiffness k (N m - ) and damping c (N s m - ) extracted from the measured second mode data ( f =6.33 khz) using the theory described in the text and Supplementary Information. This shows multi-frequency can be combined with this technique enabling additional compositional contrast channels revealing unrelated subcellular features. Topography and multi-modal observables were not taken simultaneously. Imaging parameters; k cant =77.9 pn/nm Q =.7 cant k =.33 N/m Q =3 and sp =36 nm. The scale bar on images represents 4 μm (size; 7x7 μm pixels; 56x56 acquisition time; mins).

19 igure S4. Viscoelastic tangent maps at low and high frequencies. (a) tan map at low frequency 7 khz and (b) tan map at high frequency 6 khz acquired for an adherent live fibroblast cell in culture media. (c) Reduction in viscoelastic tangent is observed by ~.3-.9.

20 Syk-GP Syk-QL-GP dherent cells a DMSO -NM-PP b 5 5 -NM-PP: Syk-QL: Syk: igure S5. ffect of Syk inhibition on cell adhesion. MD-MB-3 cells lacking Syk or expressing either Syk-GP or Syk-QL-GP (5 X 5 ) were treated with -NM- PP (5 M) or DMSO carrier alone and plated in a 6-well culture plate for 3 min. Wells were washed three-times with PBS and adherent cells visualized by light microscopy and counted. xamples of typical fields of MD-MB-3 cells expressing Syk-GP or Syk-QL-GP are illustrated in panel (a). n analysis of adherent cell counts from three separate experiments each performed in triplicate are shown in panel (b).

21 igure S6. BCC contact mechanics model fits well to the experimental data for nanomechanical properties extraction. (a-d) The residual maps showing the relationship between the experimental data and the estimated parameters. Residuals are found to be very low for all cases (~.). (e) The resnorm of the residuals is indeed small suggesting the fit is good.

22 Supplementary Movies Movie S. Progressive variation of cantilever mean deflection ( ) signal showing visualization of cytoskeleton cortical actin network on a human breast cancer cell. Movie S. Progressive variation of first harmonic oscillation amplitude ( ) signal on a human breast cancer cell.

23 Movie S3. Progressive variation of first harmonic phase lag ( ) signal on a human breast cancer cell. Movie S4. Progressive variation of nanoscale mean indentation ( ) map on a human breast cancer cell.

24 Movie S5. Progressive variation of nanoscale elastic ( a human breast cancer cell. Sneddon Cone ) modulus on Movie S6. Progressive variation of nanoscale viscous ( human breast cancer cell. Sneddon Cone ) modulus on a