Biomechanical Heterogeneity of Living Cells: Comparison between

Subscriber access provided by University of Sunderland

New Concepts at the Interface: Novel Viewpoints and Interpretations, Theory and Computations

Biomechanical Heterogeneity of Living Cells: Comparison between Atomic Force Microscopy and Finite Element Simulation Guanlin Tang, Massimiliano Galluzzi, Bokai Zhang, Yu-Lin Shen, and Florian J. Stadler Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b02211 • Publication Date (Web): 01 Oct 2018 Downloaded from http://pubs.acs.org on October 2, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Biomechanical Heterogeneity of Living Cells: Comparison between Atomic Force Microscopy and Finite Element Simulation Guanlin Tang1†, Massimiliano Galluzzi1#,2,3†, Bokai Zhang2, Yu-Lin Shen4, Florian Stadler1*

1

College of Materials Science and Engineering, Shenzhen Key Laboratory of Polymer Science and

Technology, Guangdong Research Center for Interfacial Engineering of Functional Materials, Shenzhen University, Shenzhen 518060, PR China. 2

Shenzhen Key Laboratory of Nanobiomechanics, Shenzhen Institutes of Advanced Technology, Chinese

Academy of Sciences, Shenzhen 518055, Guangdong, China. 3

formerly: CIMAINA and Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16, 20133 -

Milano, Italy. 4

Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico, USA.

† Equally contribution to this work. # formerly Shenzhen University * Corresponding author: Prof. Florian Stadler, e-mail: [email protected]

Keywords. Atomic Force Microscopy (AFM); Cell Biomechanics; Indirect Intracellular Mechanics; Finite Element Simulation; Modulus Mapping

ACS Paragon Plus Environment

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Atomic force microscopy (AFM) indentation is a popular method to characterize micromechanical properties of soft materials such as living cells. However, the mechanical data obtained from deep indentation measurements can be difficult and problematic to interpret due to complex geometry of a cell, nonlinearity of indentation contact, and constitutive relations of heterogeneous hyperelastic soft components. Living MDA-MB-231 cells were indented by spherical probes, obtaining morphological and mechanical data, which were adopted to build an accurate finite element model (FEM) for a parametric study. Initially, a 2D-axisymmetric numerical model was constructed with the main purpose of understanding the effect of geometrical and mechanical properties of constitutive parts such as cell body, nucleus, and lamellipodium. A series of FEM deformation field were directly compared with atomic force spectroscopy in order to resolve the mechanical convolution of heterogeneous parts and quantify Young’s modulus and geometry of nuclei. Furthermore, a 3D finite element model was constructed to investigate indentation events located far from axisymmetric geometry. In this framework, the joined approach FEM/AFM has provided a useful methodology and a comprehensive characterization of heterogeneous structure of living cell emphasizing the deconvolution of geometrical structure and true elastic modulus of cell nucleus.

Figure Graphical Abstract ACS Paragon Plus Environment

Page 2 of 27

Page 3 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Introduction The investigation of mechanical properties of soft biological materials (biomembranes, bacteria, living cells, and tissues) is a hot research topic in mechanobiology.1, 2 Biological functions and pathophysiological state of living cells can be correlated to local mechanical properties, for example discriminating between healthy and cancer cells.3, 4, 5, 6 Moreover, living cells can sense morphology and mechanical properties of surrounding environment reorganizing shape, motility, and cytoskeletal arrangement.7, 8, 9 Controlling these mechanotransductive events could lead to several biomedical applications, such as regenerative medicine and tissue engineering.10, 11 In this framework, atomic force microscopy (AFM) is a powerful technique able to investigate morphology and mechanical properties (such as Young’s modulus) in 1:1 correspondence. Recently, AFM was shown to be able to detect alterations of single cell rigidity correlated to pathophysiological conditions,3,

5, 6

substrate stiffness,9,

12, 13

nanotopography,14 external force

stimuli,15 as well as interaction with drugs and chemicals.16, 17 Still data analysis and interpretation require special efforts to ensure accuracy, quantification, and repeatability. For this purpose, several research groups joined to find a common acceptable protocol with application in mechanobiology.18,

19, 20

For example, recently, “standardized

nanomechanical AFM procedure” (SNAP) was introduced as a common correction developed within a large network of laboratories.19 While this is an important achievement, still standard AFM cannot overcome the intrinsic complexity of cells especially at high indentation: strong heterogeneity from nano- to microscale (external and internal) can be problematic for a quantitative data analysis. For heterogeneous systems like living cells, standard theoretical models used for nanomechanics data analysis fail to quantify correctly the mechanical properties, often requiring advanced computational modelling.13, 21, 22 Recent efforts of the authors were focused on the development of a deconvolution procedure based on coupling AFM analysis with finite element simulations and applied on model systems mimicking biological matter: heterogeneous soft hydrogels with hard inclusions.23, 24 We combined force-indentation results from AFM and FEM applied to human breast adenocarcinoma (MDA-MB-231) living cells. We used the breast adenocarcinoma cell line MDAMB-231, a well-established cellular model,25 in particular widely used for the study of cytoskeletal


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

organization and cell migration-related processes. These cells are characterized by large lamellipodia, and a highly dynamic cytoskeletal reorganization highlighting the migratory character of this metastatic cell line.26, 27 More generally, living cells can be considered as complex multi-layered systems, accounting a complex structure comprising membrane, cytoskeleton layers (actin, tubulin, intermediate filaments), nucleus, and internal organelles.28 We point out that the mechanical contribution of the external layers (at shallow indentation) is always convoluted with the inner parts (sensed at deepindentation). In our study, highly malignant MDA-MB-231 cell line represents a good compromise in heterogeneity, cytosol and cytoskeleton is less structured than healthier counterpart leading to ‘homogeneous’ cell body.29 For this reason, the difference between cell body and nucleus is well visible during indentation and FEM simulations can be designed effectively. A direct measurement of true Young’s modulus of nuclear material in situ is challenging and requiring special care. For example, Liu et al.30 measured directly membrane stiffness upon penetrating cell membrane and nuclear lamina with a sharpened AFM probe. Determination of mechanical properties for most of soft biomaterials, which present a highly complex geometry, heterogeneous features and hyperelasticity (stress-strain relationship nonlinear elastic and generally independent of strain rate), is usually difficult. . Another challenge of investigating the mechanical property of living cell is that an analytical form of force-displacement relations for hyperelastic material under indentation is not available. Therefore, a number of researchers have adopted the method of combining analytical solutions, experimental studies and FEM simulations to obtain quantitatively elastic properties of soft materials.22, 31, 32, 33 For example, Lin et al.34 proposed analytical relations based on Hertz theory for different hyperelastic models and proved that solutions obtained based on Hertz theory with spherical indenter are acceptable when the ratio of indentation depth and indenter radius is small. In one study, the uniqueness of determining material parameters of different hyperelastic models were discussed in detail by Pan

et al.32 and Valero et al.22 has introduced a correction factor when calculating the reaction force for elastic model and hyperelastic model based on simulation results by comparing the estimation of reaction force with Hertz model and those from FEM simulation based both on elastic materials and isotropic hyperelastic materials. An analytical form of load-depth relation for neo-Hookean model was introduced by Zhang et al.35 and they have quantified the difference between Hertz solution and the true nonlinear response. Barreto et al.36 have presented the role of each ACS Paragon Plus Environment

Page 4 of 27

Page 5 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

cytoskeleton (CSK) component within one single multi-structure cell on mechanical response under AFM indentation along with finite element simulation. A homogenized constitutive model of one cell, introduced by Unnikrishnan et al.37 treated the cellular structure as a fiber-reinforced composite and was later verified by simulation results and experimental data. Efremov et al.38 used a theoretical model, which solves the problem of the indentation of a linear viscoelastic halfspace by a rigid axisymmetric indenter for arbitrary load history, to extract the viscoelastic properties of various type of cells and good correlation between the simulation and experiments was found.

In this study, to resolve the mechanical convolution of various parts we developed a simplified finite element model to investigate the effects on local deformation with presence of a nucleus under AFM tip/far away from AFM tip. The model selected in the current study faces severllimitations; so far, we are neglecting several degrees of complexity such as viscoelasticity,38, 39

anisotropy,22,

40

active cortex response41 and external brush layer,42 to name few models

available in literature. Although our methodology and data analysis are open to further generalization of the FEM model, an over-describing model will have many adjustable parameters (degrees of freedom) leading to unnecessary difficulties in mechanical deconvolution of single components. Specifically, for the cell line in this study, we chose a hyperelastic composite material system consisting of soft cell body and stiff nucleus with finite thickness. Initially, a 2Daxisymmetric model was constructed with the scope of understanding the effect of geometrical and mechanical properties of constitutive parts such as cell body, nucleus and lamellipodium on indentation behavior. Furthermore, we developed a 3D finite element model to investigate indentation events with the focus of non-axisymmetric misaligned geometry, subsequently to acquire the relation between mechanical response and heterogeneous features of the composites. In this way, AFM indentation with mechanical maps and the simulation results can be used synergistically to provide insights of bio-material systems such as living cells.


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Materials and Methods Preparation of Living Cells Specimens for AFM Analysis The MDA-MB-231 cell line for AFM experiments were prepared at CIMAINA and Dipartimento di Fisica, Università degli Studi di Milano, Italy. Cells were cultured in Dulbecco’s modified eagle medium (DMEM) (Lonza) supplemented with 10% fetal bovine serum (FBS; Sigma-Aldrich), Lglutamine 5 mM, 100 units/ml penicillin and 100 units/ml streptomycin in 5% CO2, 98% airhumidified incubator (Galaxy S, RS Biotech, Irvine, California, USA) at 37°C. Cells were detached from culture dishes using a 0,25% Trypsin-EDTA in HBSS (Sigma-Aldrich), centrifuged at 1000 rpm for 5 minutes, and resuspended in the culture medium. Subcultures or culture medium exchanges were routinely established every 2nd to 3rd day into Petri dishes (diameter 10 cm). In order to thermalize the culture plates at a temperature close to 37°C, a custom fluid transparent cell for AFM measurements was used.43 The presence of the heated fluid cell does not significantly affect the transparency of the optical path, and allows to acquire measurements on the same sample for several hours (typically up to 6h) before the cells manifest signs of distress.

Mechanical Analysis by AFM Atomic Force Microscopy measurements were performed on Catalyst Bioscope (Bruker) from CIMAINA and Dipartimento di Fisica, Università degli Studi di Milano, Italy. The standard procedure used for the nanomechanical measurements on living cells and soft matter have been exhaustively discussed in a recent methodological work.43 Briefly, the measurements were performed with custom spherical colloidal probes consisting in borosilicate glass beads, locally molten onto commercial AFM tipless cantilever.44 The radius of the sphere was characterized by means of AFM reverse imaging of the colloidal probe on a spiked grating (TGT1 from NT-MDT).44 Example of tip radius calibration is shown in Figure SI1. The typical probe radius was about 5 µm, and the cantilever force constant was about 0.2 N/m. The topographic and mechanical imaging was performed with combined topography and force spectroscopy mode. In such a modality, the probe is approaching the sample vertically until a force ACS Paragon Plus Environment

Page 6 of 27

Page 7 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

trigger is reached, where force curve and compressed height (at maximum interaction force) are recorded. Force spectroscopy events are recorded on a regular grid spanning the area around living cell in order to build morphology and mechanical map in 1:1 correspondence.45 Standard parameters for the acquisition of FCs were: ramp size 5 µm, force setpoint FMAX ≈ 10nN, approaching velocity v = 43.4 µm/s, ramp rate 7.1 Hz. A total of 64X64 = 4096 force curves were typically acquired in each force volume, with 2048 points per curve, corresponding to a resolution of about 2.5 nm/point. The whole measurement comprising abovementioned 64X64X2048 points required ca. 20 min to obtain (pure measurement time without the preparation time e.g. for approaching the sample). The raw (compressed) topographic maps of the cells were built using the local z-position corresponding to the maximum setpoint force. The real uncompressed topographic map is obtained by adding the local elastic indentation.

Finite Element Modelling Simulation For rubber-like materials, bio-tissue materials and various soft material, linear elastic models cannot accurately describe their mechanical behavior, so hyperelastic models are often used. In this study, the components of living cell are modelled as incompressible hyperelastic materials, requiring a suitable constitutive model (stress–strain relationship derived from a strain energy density function) for these ideally elastic material to calculate the response of such materials. The strain energy function for spherical indentation for hyperelastic materials were first introduced by Ronald Rivlin and Melvin Mooney46 in 1940, which is still widely used and serves as a foundation of many other popular hyperelastic models. We also previously found that for elongation of hydrogels, the established neo-Hookean and Mooney-Rivlin models fit the data quite well.47 The Mooney-Rivlin model, where two material constants are required, can be expressed in strain energy density function as:

W = − 3 + − 3

(1)

Where W is strain energy, I1 and I2 are the first invariant of strain tensor, C10 and C01 are hyperelastic parameters. In our simulation framework, the neo-Hookean model, which is a special case of classic Mooney-Rivlin’s constitutive law by setting one of the parameters C01 as zero for


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 27

incompressible material, is chosen to describe the material properties of the living cell. The constitutive model in energy form is given as follows:46

W = − 3

(2)

E = 4 1 +

(3)

Where W is strain energy, I1 is the first invariant of strain tensor, C10 is hyperelastic parameter, and E is the initial Young’s modulus. ν is Poission’s ratio. With ν=0.5 for incompressible material, eq. 3 can be rewritten as:

= E/6

(4)

An axisymmetric numerical model was developed to study indentation on living cell systems with a spherical indenter, mimicking AFM experiments. Figure 1a shows one representative case, in which a cancer cell with a nucleus inside is being indented by the spherical indenter. The left boundary is treated as the symmetry axis. Although there is no intrinsic length scale in the analysis, it is convenient to associate the model with specific physical dimensions. The overall size of the entire specimen is taken as 30 μm in lateral span (radius) and 6 μm in vertical span (height). The radius of the spherical indenter is set to be 5 μm, which is equivalent to the spherical AFMindenters used in this study. During deformation, the left boundary is allowed to move only in the 2-direction (up/down). The bottom boundary is fixed to the substrate and not allowed to move in any direction. The cell surface is free to move, except when contact with the indenter is established, the surface portion engaged by the indenter is restricted to follow the indenter contour. The Young’s modulus E and Poisson’s ratio ν, used as input parameters, were: Eindenter = 160 GPa,

νindenter = 0.22. The cell body contains matrix and nucleus, both of which are considered as hyperelastic and incompressible. From AFM experimental data of a series of shallow indentation the matrix is estimated to have initial Ematrix=500 Pa, and Poisson ratio νmatrix = 0.5. The geometry and mechanical properties of nucleus (νnucleus = 0.5) were variated to produce a set of simulations to be compared with AFM data as will be explained in Results section.


Page 9 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Data analysis The complete data analysis is described in a recent work in publication, along with the opensource software ‘AFMech Suite’ developed by authors (available from the authors upon request or from https://github.com/marsdeck/AFMech-Suite).48 ‘AFMech Suite’ software was designed specifically for complex nanomechanical problems where morphology, indentation and adhesion are entangled. More details about ‘AFMech Suite’ are presented in Supporting Information. For the specific case of this work we use Hertzian contact mechanics implementing the finite thickness correction.49 The Hertz model with finite thickness correction is reported in Equation 5:

=

√ / 1

! =

√) *

+ 1.133! + 1.283! + 0.769! + 0.0975! (

(5)

Here F is the applied force, δ the indentation, ν the Poisson’s ratio, E the effective Young’s modulus of the cell, R the radius of the spherical probe and h the local thickness of sample. In the limit of χ that tends to zero, the original Hertz expression is recovered. We decided to use original expression49 for well-adherent samples so that bound between cell and substrate is strong and cell is not free to slide on substrate. The same boundary condition was used in designing the FEM model. We show in Figure S2 that adhesive interactions are negligible, ensuring the validity of the nonadhesive Hertz model. Moreover, the good overlap of approaching and retracting portions of the FCs (Figure S2) shows that viscosity is not playing a relevant role, despite the ramp frequency is somewhat higher than usual. The Hertz model requires homogeneous and isotropic samples, while living cells are definitely heterogeneous and anisotropic. When the material investigated by AFM indentation shows a certain degree of vertical heterogeneity (inclusions, layers etc.), we treat the indented specimen as a composite structure, which contains deviations from homogeneous indentation behavior and


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 27

standard contact mechanics models are failing to predict mechanical properties. To obtain information about the mechanical properties and position of the inclusion, we apply the contact mechanic model (for simplicity and calculation speed, we considered the classical Hertz model in most cases) on several floating intervals along the indentation length. This procedure is acting similarly to a derivative of force vs. indentation, resulting in enhanced visualization of different mechanical behaviors, leading to a local Apparent Young’s Modulus vs. Indentation representation and demonstrating the heterogeneity and complexity of composite material. Analogous procedure was named ‘stiffness tomography’ by Kasas and co-workers.50,

51

‘AFMech Suite’ software is

equipped with the possibility to divide the indentation curves in intervals evaluating the Apparent Young’s modulus. Although this method is useful to qualitatively visualize mechanical properties of materials with different phases, the Apparent Young’s moduli can hardly represent the absolute moduli of single parts of the composite (we always refer to Apparent Young’s Modulus throughout the text). Mechanical behavior of cells under indentation reflects the contribution of several factors such as geometries, mechanical convolution of single parts, and slippage at interface leading to highly complex mathematical problem. Beside qualitative information, Apparent Young’s modulus was used specifically to compare single AFM experimental curves with FEM simulations in order to produce quantitative results weighting all indentation intervals in the same way (comparison using Force vs. Indentation curves is more sensitive to data at high force/indentation). Stress and deformation fields from FEM are converted directly in Force (nN) vs. Indentation (nm) in order to be compared with AFM approaching force curves. Comparison is quantitatively evaluated using the relative discrepancy ∆E as in equation 6:

∆, =

-∑6 / 123 413 5 078 0 0

(6)

-∑6 / 413 5 078 0

Where EiFEM and EiAFM, represent apparent Young’s modulus of ith-interval from FEM, AFM and N represents the total number of intervals.


Page 11 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

For unknown parameters such as modulus and geometry of nucleus, position of inclusion, we run several simulations (5 – 7 sets). The ‘array’ of simulation is generally built variating a single unknown quantity around the most probable value estimated from AFM morphology and standard mechanical map. After loading the entire array of simulated FCs in ‘AFMech Suite’, the FEM curve relative to the parameter that minimizes ∆E is automatically selected and highlighted.

Results and Discussion The possibility to combine AFM and finite element modelling simulations is particularly useful to estimate quantitatively the mechanical properties of complex systems such as living cells. MDAMB-231 cells in vitro are known to display a variety of morphological forms52 and we noticed a biological variation in the average Young’s moduli reflecting the nature of the MDA-MB-231 cell line that is characterized by a high diversity and structural reorganization.53 Differences in the baseline do not affect the conclusions of this work, since every set of finite element simulations is built ad-hoc for every AFM experimental data. We show how 2D-axisymmetric model and refined 3D model predict AFM experimental data leading to quantification of mechanical properties of heterogeneous structures

The model of living cells The geometrical property of a living cell is variable and can change with time due to the nature of highly malignant metastatic cancer. When investigating the mechanical properties of a living cell, many factors can contribute to the measured indentation data, such as the height and lateral span of the cell, the size and stiffness of the nucleus inside, and the relative location of the nucleus. A comprehensive model was built to perform indentation simulation with different parameters to find the main deciding factors. According to Figure 1a of a testing specimen, the height H and lateral span of the single living cell L was estimated at 6 μm and 60 μm (30μm in axisymmetric model). The radius of a spherical nucleus Rnucleus was set between 1.5μm and 2.5 μm, while Enucleus was variated between 0.5 kPa and 2.5 kPa. The force indentation curves from simulation results with various configurations as described are summarized in Figure 1c. With the assumption that ACS Paragon Plus Environment

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

the nucleus and the matrix are perfectly bonded and deform as one unity, one can tell that the force-indentation response is sensitive to both the size and stiffness of the nucleus, when it is directly underneath the indenter as shown in Figure 1c. This finding provides a guideline to link the geometrical and mechanical property of the cell with the overall mechanical behavior when a living cell is indented in AFM experiment. Next, simulations in which a spherical shape of nucleus is replaced by an elliptical shape, are considered to investigate the effects of shape of the nucleus on overall force-indentation response. The influence was found to be negligible compared with experimental noise of AFM. Furthermore, the influence of depth at which the nucleus is residing along vertical axis was also studied and we have discovered that: the effect of the location of the nucleus (relatively closer to the indenter or to the bottom of the sample) is also negligible. It is worth mentioning that the relative location of a hard particle inside an “infinite” soft gel matrix has a significant influence on the mechanical response in previous study.23, This effects with living cell model on mechanical behavior is opposite to the findings with “infinite” thickness model, hence, the conclusion regarding negligible effects of the location at which the nucleus is residing is valid within current finite thickness model, while it may not be applicable to other cases. Although the size of nucleus (volume) and stiffness of nucleus do introduce a big difference in reaction force with indentation on cell and they will be addressed in the following, corresponding sections, while the shape and exact depth of the nucleus will not be discussed. In addition, we have investigated indentation simulation with different boundary conditions (no-slip and free-slip along cellsubstrate interface) in 2D model54 with findings that the mechanical responses differ significantly (30%-40%) at deep indentation around half depth of total height of the cell. Figure 1b shows the stress field for 2D-axisymmetric model of cell + nucleus system at maximum indentation depth of 1.5 μm. The nucleus geometry (Rnucleus= 2 μm) can be easily spotted in the region where a large color contrast exists. As expected, the deformation evolution becomes more complex with the existence of a nucleus inside the matrix. The matrix region sandwiched between the indenter and nucleus is severely deformed. The upper region of the nucleus has also experienced larger deformation compared to the lower portion.


Page 12 of 27

Page 13 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 1. (a) Representation showing an axisymmetric model of a living cell with a nucleus inside being indented on with a spherical indenter in finite element simulation. (b) Von Mises stress contour plots at indentation depth of 1.5 μm. (c) Force-indentation curves during indentation of cell body/nucleus composite material system with various properties of nucleus. Three-dimensional modeling has also been carried out, to compare the response between the perfectly aligned indentation (indenting directly on top of the underlying nucleus) and misaligned indentation (indenting on the area near the nucleus). The offset width r is defined as the width of the centerline of spherical indenter and the centerline of the spherical nucleus as shown in Figure 2a.


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The indentation responses are plotted in Figure 2b, in which it can be seen that the force indentation response is sensitive to the fact whether the nucleus is directly underneath the indenter. Indenting off-center does generate a much smaller reaction force compared with perfectly aligned indentation, which can be further explained by examining the stress contour plots. Figure 2c-h shows the stress components along cross-sections that contains both centerlines of the indenter and the nucleus in the 3D simulations. From evolution of in plane shear stress S12 in Figure 2c-d, it is obvious that the shear stress is symmetric in the perfectly aligned indentation case and it becomes asymmetric when there is an offset width r. It is also noticed that the existence of a nucleus altered the whole structure of the sample under the probe, i.e., the probe can detect some hard inclusion at one side and a slightly tilted contact surface, and the largest S12 magnitude in the misaligned case (in the top central region of the nucleus) is significantly greater than that in the perfectly aligned case. This asymmetric shear stress would generate a tendency for the nucleus to further move away from the indenter, in addition the nucleus is being pushed towards left partly due to its residing location, i.e., high S22 compression to the right of the nucleus as shown in Fig. 2f. From the magnitude of normal stress S22 along indentation axis as shown in Figure 2e-f, one can tell that the normal stress along the indenting direction is lower in the misaligned indentation case, which directly contribute to the lower reaction force measured in experiments. The von Mises stress is a scalar value computed from stress tensor and it is generally used as the criterion of yielding from elastic deformation regime to plastic deformation regime. In our case, the contour plots of von Mises effective stress in Figure 2g-h show that both the nucleus and surrounding matrix are more highly stressed in the perfectly aligned case. When there is an offset, a larger matrix (weaker) region is responsible for absorbing the deformation, which also contributes to the reduced indentation force.


Page 14 of 27

Page 15 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 2. (a) Representation of a 3D model showing misalignment between the nucleus and the indenter in finite element simulation. (b) Force-indentation curves during indentation of cell body/nucleus composite material system with perfectly aligned setup and various offset value in misaligned setup. Shear stress S12 contour plots of (c) perfectly aligned indentation and (d) misaligned indentation with offset value δ = 2 µm at indentation depth of 900 nm. Normal stress S22 (along vertical axis 2) contour plots of (e) perfectly aligned indentation and (f) misaligned indentation with offset value δ = 2 µm at indentation depth of 900 nm. Von Mises stress contour plots of (g) perfectly aligned indentation and (h) misaligned indentation with offset value δ = 2 µm at indentation depth of 900 nm.


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 27

AFM experimental data and comparison with FEM model Force spectroscopy analysis was performed using custom micrometrical spherical probes as described in Materials and Methods. Such large probes granted a superior performance for quantitative nanomechanical experiments on living cells (generally, for all specimens with Young’s modulus inferior to 10 kPa) because of the well-defined geometry and reduced applied pressure, although decreasing lateral resolution (either in morphology and mechanical mapping).55 Using a larger micrometer-sized probe in nanoindentation experiments allowed a robust statistical averaging over a mesoscopic interaction area between probe and surface of cell. This effect of local averaging is particularly useful to investigate the mechanical properties of cytoskeleton in living cells. Micrometric spherical probes were selected specifically to average local features on biomembranes such as glycocanes, brushes, and membrane proteins, but maintaining enough spatial resolution to focus on mechanical response of cell body.48 Other disadvantages in using colloidal probes are related to finite thickness effect more enhanced using larger probes, therefore a correction for thin layers on hard substrate is necessary.49 As shown in cell morphology of Figure 3a, the lateral resolution of the probe is enough to distinguish the cell shape from substrate highlighting different components such as lamellipodium and cell body. Previous studies of our group were focused mainly on mechanical response of external layers like membrane and actin cytoskeleton, as they are the most sensitive parts influenced by environmental conditions14,

56

or external chemicals.43,

57

Force curves were

considered only for shallow indentation (0 – 500 nm compared with 5000 nm radius), where Hertz model (with finite thickness correction) is acceptable, leading to quantitative results. Interestingly, the effect of cytoskeleton-targeting drug, such as Cytochalasin-D, was tested at shallow indentation focusing on external layers of cytoskeleton. This drug is triggering depolymerization of actin causing morphological changes and lowering the average Young’s modulus.43 In particular, the accumulation points of actin cytoskeleton (for example focal adhesion) tend to disappear along with the intrinsic heterogeneous structure, visible as sharpening of histogram during quantitative analysis. In this work, we analyze force curves at deeper indentation regime (1200 – 1700 nm compared with 5000 nm radius), where effectiveness of Hertz model is decreased. Moreover, as demonstrated in Figure 3c, Young’s modulus of the intracellular parts, especially the nucleus, ACS Paragon Plus Environment

Page 17 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

becomes evident (i.e. stiffer than surrounding cell body), meaning that vertical heterogeneity plays an important role in Young’s modulus at deep indentation. The true Young’s moduli of the internal parts are hard to be quantified directly from AFM imaging because of mechanical convolution of different parts (structural heterogeneity). In particular, a simple and operative contact mechanical model is not available because of intrinsic complex geometry. Using a methodology and software recently developed by our group,48 we extracted properties from AFM force volume on living cell using nano-mechanical analysis at shallow indentation. In our case, morphology at zero force (uncompressed morphology) and Young’s modulus of cell body were fixed during construction of FEM model. After these starting assumptions, an array of simulations was built to investigate properties of unknown, hidden parts such as nucleus size, position, and intrinsic true Young’s modulus. The comparison between FEM and AFM is performed by minimizing ∆E in Equation 6, therefore selecting the nearest simulation to AFM data. A plug-in in AFMech Suite software allows to perform easily and quickly the comparison operation (see Supporting Information 2). In Figure 3b we show AFM force curves chosen on the cell body (1) and on top of nucleus (2), while a continuous line represents the best simulation of explorative set. We explored elastic modulus of nucleus between 500 Pa and 5000 Pa, while the nucleus radius size was varied between 1.5 µm and 2.5 µm. The most similar simulation was automatically highlighted, showing Enucleus = 2000 Pa and Rnucleus = 2 µm.


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 3: Results of mechanical analysis for MDA-MB-231 (a) morphology map at zero force (b) Force vs. Indentation curves for points 1 and 2, comparing AFM results and FEM simulations, (c) Young’s modulus map in logarithmic scale at high indentation (70% - 100% of maximum value) (d) Apparent Young’s modulus vs. Indentation for points 1 and 2, comparing AFM results and FEM simulations.

To avoid repetition in the main text, we show a similar analysis on a second MDA-MB-231 cells in Supporting Information, Figure SI.3. From AFM morphology a different geometry was used (40 µm X 40 µm x 5 µm; nucleus radius 1.5 µm) but same modulus for cell body (E = 500 Pa), leading to similar result: nucleus shows a Young’s modulus (E = 2000 Pa) harder than surrounding cell body. Mechanical map at high indentation (70 % - 100 %) from Figure 3c shows only an increase of Young’s modulus at +50% compared with cell body, while after mechanical deconvolution through FEM/AFM simulation highlights an increase up to +200%.


Page 18 of 27

Page 19 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

As explained previously, a 3D FEM model was built in order to generalize the 2D-axisymmetric simulations and remove the constraint of a symmetric geometry. In this way, every force curve from AFM map could be simulated accurately taking explicitly into account its position within the cell. Figure 4a shows a tomography for a row crossing nucleus and cellular body, where a point on top of nucleus and a point with 5µm offset were selected. Tomography maintains the proportional size of the cell after morphology evaluation, so that every point on the line represents an Apparent Young’s modulus vs. Indentation curve depicted with a color scale. For example, repeating this operation for each force curve in force volume, we obtained an object defined as ‘force hyperspectrum’, a 3D matrix where each point represents the apparent Young’s modulus in the indentation volume. In the case of what we call ‘tomography’, the section represents a vertical (or normal) slice from the ‘force hyperspectrum’, another section can be planar (or parallel) obtaining mechanical maps like Figure 3c.


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 4. Comparison between AFM results and 3D FEM simulations (a) Apparent Young’s Modulus tomography from a line crossing nucleus and cell body of Figure 3c. Red arrows indicate position of indentation ‘centered’ and ‘5µm offset’. (b) Force vs. Indentation curves for points ‘centered’ and ‘5µm offset’, comparing AFM results and 3D-FEM simulations, (c) Apparent Young’s modulus vs. Indentation built from force curves in image b.

The selected points on the tomography line are evidenced in Figure 4b (Force vs. indentation) and Figure 4c (Apparent Young’s modulus vs. Indentation). The results of comparison, showing good agreement between AFM and FEM, highlight again a nucleus 4 times stiffer than surrounding cell body. Moreover, 3D simulations predict a lateral shift of nucleus during probe indentation as


Page 20 of 27

Page 21 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

shown in Figure 2. Lateral shifts cannot be visualized directly during AFM experiments although FEM comparison confirmed the existence. As we explained in previous section, the asymmetric shear stress generated by indention in misaligned model is responsible for pushing the nucleus to move further away from the indenter. Lateral shift is a result of stiffer nucleus resisting deformability imposed by probe indenting the cell surface. In the case of our study, nuclear region after mechanical deconvolution is 4 times stiffer than surrounding cell body. This finding is consistent with our previous publication,30 where the nuclei of both RT4 and T34 cell lines were pierced by sharp AFM probes, exhibiting significantly higher Young’s moduli than the cell membrane (8.4 ± 1.02 vs. 5.33 ± 0.73 kPa for RT4; 5.67 ± 0.48 vs. 3.42 ± 0.26 kPa for T24). The different magnitude between our results and the publication is probably due to the different cell lines, indentation strategy (penetration) and mechanical deconvolution. Higher Young’s modulus of nucleus is connected with internal higher stiffness and it should be ascribed to the nucleoplasm surrounding chromatin preventing the nucleus deformation. Swift et al.58, using micropipette aspiration, have shown as nuclear lamin-A protein is responsible for nuclear mechanical properties, in particular abundance of such protein confers higher Young’s modulus impeding nuclear deformation under external stress. Next, extension of our approach will be the application of this methodology to problems with higher complexity, for examples cells supported on hydrogels with different stiffness or different cell lines where adhesion between probe and sample play an important role. For these complex systems the possibility to deconvolute single mechanical elements will be helpful to focus and quantify biological effects such as reorganization of cytoskeleton or probe/membrane adhesion dynamics.

Conclusions We have carried out a systematic investigation of mechanical properties of living MDA-MB231 cells accounting intrinsic structural heterogeneity. Force spectroscopy by AFM was used with particular emphasis for deep indentation to be sensitive to internal heterogeneity. In order to interpret and analyze such data we used finite element simulation in 2D-axisymmetric and 3D ACS Paragon Plus Environment

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

configuration. We derive the model using shallow indentation AFM data, while variating unknown parameters such as stiffness and geometry of internal parts. As an example of reconstruction of heterogeneous structure, we applied the methodology to AFM force volume data of living cells quantifying modulus and geometry of nucleus. We conclude that nuclei of adherent MDA-MB-231 in standard conditions are 3-4 times stiffer than surrounding cell body. 3D simulations evidenced the nucleus shifting laterally during asymmetric indentation, underlining how a stiffer nucleus can prevent deformability (and therefore damage) caused by external force stimuli.

Associated Content Supporting Information. Colloidal probes radius calibration , Adhesion analysis , Additional Mechanical Data, Analysis Software: AFMech Suite, References.

Acknowledgements The authors thank Alessandro Podestà, Carsten Schulte, Cristina Lenardi and Paolo Milani for support in the cell-biology laboratory of University of Milano, CIMaINa. M.G. acknowledges the Shenzhen Science and Technology Innovation Committee (JCYJ20170818160503855) for support. FJS would like to thank the National Science Foundation of China (21574086), Shenzhen Sci & Tech research grant (ZDSYS201507141105130), Shenzhen City Science and Technology Plan Project (JCYJ20160520171103239).

Conflict of Interest The authors declare no conflict of interest.


Page 22 of 27

Page 23 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

References 1. Alessandrini, A.; Facci, P. AFM: a versatile tool in biophysics. Measurement Science and Technology 2005, 16 (6), R65-R92. 2. Kuznetsova, T. G.; Starodubtseva, M. N.; Yegorenkov, N. I.; Chizhik, S. A.; Zhdanov, R. I. Atomic force microscopy probing of cell elasticity. Micron 2007, 38 (8), 824-33. 3. Rianna, C.; Radmacher, M. Cell Mechanics as a Marker for Diseases: Biomedical Applications of AFM. Physics of Cancer: Interdisciplinary Problems and Clinical Applications (Pc'16) 2016, 1760. 4. Zemla, J.; Danilkiewicz, J.; Orzechowska, B.; Pabijan, J.; Seweryn, S.; Lekka, M. Atomic force microscopy as a tool for assessing the cellular elasticity and adhesiveness to identify cancer cells and tissues. Semin Cell Dev Biol 2017. 5. Lekka, M. Discrimination Between Normal and Cancerous Cells Using AFM. BioNanoScience 2016, 6 (1), 65-80. 6. Plodinec, M.; Loparic, M.; Monnier, C. A.; Obermann, E. C.; Zanetti-Dallenbach, R.; Oertle, P.; Hyotyla, J. T.; Aebi, U.; Bentires-Alj, M.; Lim, R. Y.; Schoenenberger, C. A. The nanomechanical signature of breast cancer. Nat Nanotechnol 2012, 7 (11), 757-65. 7. Jorba, I.; Uriarte, J. J.; Campillo, N.; Farré, R.; Navajas, D. Probing Micromechanical Properties of the Extracellular Matrix of Soft Tissues by Atomic Force Microscopy. Journal of Cellular Physiology 2017, 232 (1), 19-26. 8. Alcaraz, J.; Otero, J.; Jorba, I.; Navajas, D. Bidirectional mechanobiology between cells and their local extracellular matrix probed by atomic force microscopy. Seminars in Cell & Developmental Biology 2017. 9. Rianna, C.; Kumar, P.; Radmacher, M. The Role of the Microenvironment in the Biophysics of Cancer. Seminars in Cell & Developmental Biology 2017. 10. Marrese, M.; Guarino, V.; Ambrosio, L. Atomic Force Microscopy: A Powerful Tool to Address Scaffold Design in Tissue Engineering. J Funct Biomater 2017, 8 (1), 7. 11. Engel, E.; Michiardi, A.; Navarro, M.; Lacroix, D.; Planell, J. A. Nanotechnology in regenerative medicine: the materials side. Trends Biotechnol 2008, 26 (1), 39-47. 12. Tee, S. Y.; Fu, J. P.; Chen, C. S.; Janmey, P. A. Cell Shape and Substrate Rigidity Both Regulate Cell Stiffness. Biophysical Journal 2011, 100 (5), L25-L27. 13. Vichare, S.; Sen, S.; Inamdar, M. M. Cellular mechanoadaptation to substrate mechanical properties: contributions of substrate stiffness and thickness to cell stiffness measurements using AFM. Soft Matter 2014, 10 (8), 1174-81.


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

14. Schulte, C.; Rodighiero, S.; Cappelluti, M. A.; Puricelli, L.; Maffioli, E.; Borghi, F.; Negri, A.; Sogne, E.; Galluzzi, M.; Piazzoni, C.; Tamplenizza, M.; Podesta, A.; Tedeschi, G.; Lenardi, C.; Milani, P. Conversion of nanoscale topographical information of cluster-assembled zirconia surfaces into mechanotransductive events promotes neuronal differentiation. J Nanobiotechnology 2016, 14 (1), 18. 15. Weng, Y.; Yan, F.; Chen, R.; Qian, M.; Ou, Y.; Xie, S.; Zheng, H.; Li, J. PIEZO channel protein naturally expressed in human breast cancer cell MDA-MB-231 as probed by atomic force microscopy. AIP Advances 2018, 8 (5), 055101. 16. Rotsch, C.; Radmacher, M. Drug-Induced Changes of Cytoskeletal Structure and Mechanics in Fibroblasts: An Atomic Force Microscopy Study. Biophysical Journal 2000, 78 (1), 520-535. 17. Kasas, S.; Wang, X.; Hirling, H.; Marsault, R.; Huni, B.; Yersin, A.; Regazzi, R.; Grenningloh, G.; Riederer, B.; Forro, L.; Dietler, G.; Catsicas, S. Superficial and deep changes of cellular mechanical properties following cytoskeleton disassembly. Cell Motil Cytoskeleton 2005, 62 (2), 124-32. 18. Sokolov, I.; Dokukin, M. E.; Guz, N. V. Method for quantitative measurements of the elastic modulus of biological cells in AFM indentation experiments. Methods 2013, 60 (2), 202-13. 19. Schillers, H.; Rianna, C.; Schäpe, J.; Luque, T.; Doschke, H.; Wälte, M.; Uriarte, J. J.; Campillo, N.; Michanetzis, G. P. A.; Bobrowska, J.; Dumitru, A.; Herruzo, E. T.; Bovio, S.; Parot, P.; Galluzzi, M.; Podestà, A.; Puricelli, L.; Scheuring, S.; Missirlis, Y.; Garcia, R.; Odorico, M.; Teulon, J.-M.; Lafont, F.; Lekka, M.; Rico, F.; Rigato, A.; Pellequer, J.-L.; Oberleithner, H.; Navajas, D.; Radmacher, M. Standardized Nanomechanical Atomic Force Microscopy Procedure (SNAP) for Measuring Soft and Biological Samples. Sci Rep-Uk 2017, 7 (1), 5117. 20. Wu, P. H.; Aroush, D. R.; Asnacios, A.; Chen, W. C.; Dokukin, M. E.; Doss, B. L.; Durand-Smet, P.; Ekpenyong, A.; Guck, J.; Guz, N. V.; Janmey, P. A.; Lee, J. S. H.; Moore, N. M.; Ott, A.; Poh, Y. C.; Ros, R.; Sander, M.; Sokolov, I.; Staunton, J. R.; Wang, N.; Whyte, G.; Wirtz, D. A comparison of methods to assess cell mechanical properties. Nat Methods 2018. 21. Ding, Y.; Xu, G.-K.; Wang, G.-F. On the determination of elastic moduli of cells by AFM based indentation. Sci Rep 2017, 7, 45575. 22. Valero, C.; Navarro, B.; Navajas, D.; Garcia-Aznar, J. M. Finite element simulation for the mechanical characterization of soft biological materials by atomic force microscopy. J Mech Behav Biomed Mater 2016, 62, 222-35. 23. Tang, G.; Galluzzi, M.; Biswas, C. S.; Stadler, F. J. Investigation of micromechanical properties of hard sphere filled composite hydrogels by atomic force microscopy and finite element simulations. J Mech Behav Biomed Mater 2018, 78, 496-504. 24. Esfahani, E. N.; Ma, F. Y.; Wang, S. Y.; Ou, Y.; Yang, J. H.; Li, J. Y. Quantitative nanoscale mapping of three-phase thermal conductivities in filled skutterudites via scanning thermal microscopy. Natl Sci Rev 2018, 5 (1), 59-69.


Page 24 of 27

Page 25 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

25. Cailleau, R.; Olive, M.; Cruciger, Q. V. J. Long-Term Human Breast Carcinoma Cell Lines of Metastatic Origin - Preliminary Characterization. In Vitro Cell Dev B 1978, 14 (11), 911-915. 26. Isogai, T.; van der Kammen, R.; Leyton-Puig, D.; Kedziora, K. M.; Jalink, K.; Innocenti, M. Initiation of lamellipodia and ruffles involves cooperation between mDia1 and the Arp2/3 complex. Journal of Cell Science 2015, 128 (20), 3796-3810. 27. Frittoli, E.; Palamidessi, A.; Marighetti, P.; Confalonieri, S.; Bianchi, F.; Malinverno, C.; Mazzarol, G.; Viale, G.; Martin-Padura, I.; Garré, M.; Parazzoli, D.; Mattei, V.; Cortellino, S.; Bertalot, G.; Di Fiore, P. P.; Scita, G. A RAB5/RAB4 recycling circuitry induces a proteolytic invasive program and promotes tumor dissemination. The Journal of Cell Biology 2014, 206 (2), 307-328. 28. Kaushik, G.; Fuhrmann, A.; Cammarato, A.; Engler, A. J. In situ mechanical analysis of myofibrillar perturbation and aging on soft, bilayered Drosophila myocardium. Biophys J 2011, 101 (11), 2629-37. 29. Hu, J.; Zhou, Y.; Obayemi, J. D.; Du, J.; Soboyejo, W. O. An investigation of the viscoelastic properties and the actin cytoskeletal structure of triple negative breast cancer cells. J Mech Behav Biomed 2018, 86, 1-13. 30. Liu, H.; Wen, J.; Xiao, Y.; Liu, J.; Hopyan, S.; Radisic, M.; Simmons, C. A.; Sun, Y. In Situ Mechanical Characterization of the Cell Nucleus by Atomic Force Microscopy. ACS Nano 2014, 8 (4), 3821-3828. 31. Madireddy, S.; Sista, B.; Vemaganti, K. Bayesian calibration of hyperelastic constitutive models of soft tissue. J Mech Behav Biomed Mater 2016, 59, 108-27. 32. Pan, Y.; Zhan, Y.; Ji, H.; Niu, X.; Zhong, Z. Can hyperelastic material parameters be uniquely determined from indentation experiments? RSC Adv. 2016, 6 (85), 81958-81964. 33. Lin, Y.-Y.; Chen, H.-Y. Effect of large deformation and material nonlinearity on the JKR (Johnson–Kendall–Roberts) test of soft elastic materials. Journal of Polymer Science Part B: Polymer Physics 2006, 44 (19), 2912-2922. 34. Lin, D. C.; Shreiber, D. I.; Dimitriadis, E. K.; Horkay, F. Spherical indentation of soft matter beyond the Hertzian regime: numerical and experimental validation of hyperelastic models. Biomech Model Mechan 2009, 8 (5), 345-358. 35. Zhang, M. G.; Cao, Y. P.; Li, G. Y.; Feng, X. Q. Spherical indentation method for determining the constitutive parameters of hyperelastic soft materials. Biomech Model Mechanobiol 2014, 13 (1), 1-11. 36. Barreto, S.; Clausen, C. H.; Perrault, C. M.; Fletcher, D. A.; Lacroix, D. A multi-structural single cell model of force-induced interactions of cytoskeletal components. Biomaterials 2013, 34 (26), 6119-26. 37. Unnikrishnan, G. U.; Unnikrishnan, V. U.; Reddy, J. N. Constitutive material modeling of cell: a micromechanics approach. J Biomech Eng 2007, 129 (3), 315-23.


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

38. Efremov, Y. M.; Wang, W.-H.; Hardy, S. D.; Geahlen, R. L.; Raman, A. Measuring nanoscale viscoelastic parameters of cells directly from AFM force-displacement curves. Sci Rep-Uk 2017, 7 (1), 1541. 39. Fischer-Friedrich, E.; Toyoda, Y.; Cattin, C. J.; Muller, D. J.; Hyman, A. A.; Julicher, F. Rheology of the Active Cell Cortex in Mitosis. Biophys J 2016, 111 (3), 589-600. 40. Vishavkarma, R.; Raghavan, S.; Kuyyamudi, C.; Majumder, A.; Dhawan, J.; Pullarkat, P. A. Role of Actin Filaments in Correlating Nuclear Shape and Cell Spreading. Plos One 2014, 9 (9). 41. Fischer-Friedrich, E. Active Prestress Leads to an Apparent Stiffening of Cells through Geometrical Effects. Biophys J 2018, 114 (2), 419-424. 42. Iyer, S.; Gaikwad, R. M.; Subba-Rao, V.; Woodworth, C. D.; Sokolov, I. Atomic force microscopy detects differences in the surface brush of normal and cancerous cells. Nat Nanotechnol 2009, 4 (6), 389-93. 43. Puricelli, L.; Galluzzi, M.; Schulte, C.; Podesta, A.; Milani, P. Nanomechanical and topographical imaging of living cells by atomic force microscopy with colloidal probes. Rev Sci Instrum 2015, 86 (3), 033705. 44. Indrieri, M.; Podesta, A.; Bongiorno, G.; Marchesi, D.; Milani, P. Adhesive-free colloidal probes for nanoscale force measurements: Production and characterization. Rev Sci Instrum 2011, 82 (2). 45. Butt, H.-J.; Cappella, B.; Kappl, M. Force measurements with the atomic force microscope: Technique, interpretation and applications. Surface Science Reports 2005, 59 (1), 1-152. 46. Mooney, M. A Theory of Large Elastic Deformation. Journal of Applied Physics 1940, 11 (9), 582-592. 47. Stadler, F. J.; Friedrich, T.; Kraus, K.; Tieke, B.; Bailly, C. Elongational rheology of NIPAMbased hydrogels. Rheologica Acta 2013, 52 (5), 413-423. 48. Galluzzi, M.; Tang, G.; Biswas, C. S.; Zhao, J.; Chen, S.; Stadler, F. J. Atomic force microscopy methodology and AFMech Suite software for nanomechanics on heterogeneous soft materials. Nature Communication 2018, Just Accepted, in press. 49. Dimitriadis, E. K.; Horkay, F.; Maresca, J.; Kachar, B.; Chadwick, R. S. Determination of Elastic Moduli of Thin Layers of Soft Material Using the Atomic Force Microscope. Biophysical Journal 2002, 82 (5), 2798-2810. 50. Roduit, C.; Longo, G.; Benmessaoud, I.; Volterra, A.; Saha, B.; Dietler, G.; Kasas, S. Stiffness tomography exploration of living and fixed macrophages. J Mol Recognit 2012, 25 (5), 241-246. 51. Roduit, C.; Sekatski, S.; Dietler, G.; Catsicas, S.; Lafont, F.; Kasas, S. Stiffness Tomography by Atomic Force Microscopy. Biophysical Journal 2009, 97 (2), 674-677.


Page 26 of 27

Page 27 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

52. Brinkley, B. R.; Beall, P. T.; Wible, L. J.; Mace, M. L.; Turner, D. S.; Cailleau, R. M. Variations in Cell Form and Cytoskeleton in Human Breast Carcinoma Cells in Vitro. Cancer Res 1980, 40 (9), 3118-3129. 53. Nguyen, A.; Yoshida, M.; Goodarzi, H.; Tavazoie, S. F. Highly variable cancer subpopulations that exhibit enhanced transcriptome variability and metastatic fitness. Nature communications 2016, 7, 11246. 54. Tang, G.; Galluzzi, M.; Biswas, C. S.; Stadler, F. J. Investigation of micromechanical properties of hard sphere filled composite hydrogels by atomic force microscopy and finite element simulations. Journal of the Mechanical Behavior of Biomedical Materials 2018, 78, 496504. 55. Galluzzi, M.; Biswas, C. S.; Wu, Y.; Wang, Q.; Du, B.; Stadler, F. J. Space-resolved quantitative mechanical measurements of soft and supersoft materials by atomic force microscopy. NPG Asia Materials 2016, 8 (11), e327. 56. Schulte, C.; Podestà, A.; Lenardi, C.; Tedeschi, G.; Milani, P. Quantitative Control of Protein and Cell Interaction with Nanostructured Surfaces by Cluster Assembling. Accounts of Chemical Research 2017. 57. Schulte, C.; Ferraris, G. M.; Oldani, A.; Galluzzi, M.; Podesta, A.; Puricelli, L.; de Lorenzi, V.; Lenardi, C.; Milani, P.; Sidenius, N. Lamellipodial tension, not integrin/ligand binding, is the crucial factor to realise integrin activation and cell migration. Eur J Cell Biol 2016, 95 (1), 1-14. 58. Swift, J.; Ivanovska, I. L.; Buxboim, A.; Harada, T.; Dingal, P. C. D. P.; Pinter, J.; Pajerowski, J. D.; Spinler, K. R.; Shin, J.-W.; Tewari, M.; Rehfeldt, F.; Speicher, D. W.; Discher, D. E. Nuclear LaminA Scales with Tissue Stiffness and Enhances Matrix-Directed Differentiation. Science 2013, 341 (6149).


Biomechanical Heterogeneity of Living Cells: Comparison between

Recommend Documents