Standardized Nanomechanical Atomic Force Microscopy Procedure (SNAP) for Measuring Soft and Biological Samples

We present a procedure that allows a reliable determination of the elastic (Young’s) modulus of soft samples, including living cells, by atomic force microscopy (AFM). The standardized nanomechanical AFM procedure (SNAP) ensures the precise adjustment of the AFM optical lever system, a prerequisite for all kinds of force spectroscopy methods, to obtain reliable values independent of the instrument, laboratory and operator. Measurements of soft hydrogel samples with a well-defined elastic modulus using different AFMs revealed that the uncertainties in the determination of the deflection sensitivity and subsequently cantilever’s spring constant were the main sources of error. SNAP eliminates those errors by calculating the correct deflection sensitivity based on spring constants determined with a vibrometer. The procedure was validated within a large network of European laboratories by measuring the elastic properties of gels and living cells, showing that its application reduces the variability in elastic moduli of hydrogels down to 1%, and increased the consistency of living cells elasticity measurements by a factor of two. The high reproducibility of elasticity measurements provided by SNAP could improve significantly the applicability of cell mechanics as a quantitative marker to discriminate between cell types and conditions.

[1]  D. Navajas,et al.  Cell dynamic adhesion and elastic properties probed with cylindrical atomic force microscopy cantilever tips , 2007, Journal of molecular recognition : JMR.

[2]  D. A. Billings,et al.  An approximate solution for the contact area and elastic compliance of a smooth punch of arbitrary shape , 1990 .

[3]  Ellen Kuhl,et al.  The emergence of extracellular matrix mechanics and cell traction forces as important regulators of cellular self-organization , 2015, Biomechanics and modeling in mechanobiology.

[4]  Gus Gurley,et al.  Short cantilevers for atomic force microscopy , 1996 .

[5]  S. Sen,et al.  Matrix Elasticity Directs Stem Cell Lineage Specification , 2006, Cell.

[6]  Manfred Radmacher,et al.  Comparison of mechanical properties of normal and malignant thyroid cells. , 2012, Micron.

[7]  M. Radmacher,et al.  Cell mechanics as a marker for diseases: Biomedical applications of AFM , 2016 .

[8]  G. G. Bilodeau,et al.  Regular Pyramid Punch Problem , 1992 .

[9]  P. Hansma,et al.  An atomic-resolution atomic-force microscope implemented using an optical lever , 1989 .

[10]  Jean-Luc Pellequer,et al.  Past, present and future of atomic force microscopy in life sciences and medicine , 2007, Journal of molecular recognition : JMR.

[11]  C. Lim,et al.  AFM indentation study of breast cancer cells. , 2008, Biochemical and biophysical research communications.

[12]  J. Hutter.  Comment on tilt of atomic force microscope cantilevers: effect on spring constant and adhesion measurements. , 2005, Langmuir : the ACS journal of surfaces and colloids.

[13]  Z. Stachura,et al.  Elasticity of normal and cancerous human bladder cells studied by scanning force microscopy , 1999, European Biophysics Journal.

[14]  Manfred Radmacher,et al.  Softening of the actin cytoskeleton by inhibition of myosin II , 2008, Pflügers Archiv - European Journal of Physiology.

[15]  Jason Cleveland,et al.  Finite optical spot size and position corrections in thermal spring constant calibration , 2004 .

[16]  M. Sheetz,et al.  Local force and geometry sensing regulate cell functions , 2006, Nature Reviews Molecular Cell Biology.

[17]  Arvind Raman,et al.  Uncertainty quantification in nanomechanical measurements using the atomic force microscope , 2011, Nanotechnology.

[18]  Hans-Jürgen Butt,et al.  Calculation of thermal noise in atomic force microscopy , 1995 .

[19]  H. Gaub,et al.  Interlaboratory round robin on cantilever calibration for AFM force spectroscopy. , 2011, Ultramicroscopy.

[20]  Kuo-Kang Liu,et al.  Optical tweezers for single cells , 2008, Journal of The Royal Society Interface.

[21]  David C Lin,et al.  Robust strategies for automated AFM force curve analysis--I. Non-adhesive indentation of soft, inhomogeneous materials. , 2007, Journal of biomechanical engineering.

[22]  W. Kraus,et al.  Endothelial, cardiac muscle and skeletal muscle exhibit different viscous and elastic properties as determined by atomic force microscopy. , 2001, Journal of biomechanics.

[23]  Jon R. Pratt,et al.  Precision and accuracy of thermal calibration of atomic force microscopy cantilevers , 2006 .

[24]  Manfred Radmacher,et al.  Direct, high-resolution measurement of furrow stiffening during division of adherent cells , 2001, Nature Cell Biology.

[25]  F Guilak,et al.  Viscoelastic properties of chondrocytes from normal and osteoarthritic human cartilage , 2000, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[26]  P. Milani,et al.  Nanomechanical and topographical imaging of living cells by atomic force microscopy with colloidal probes. , 2014, The Review of scientific instruments.

[27]  C. Lim,et al.  Biomechanics approaches to studying human diseases. , 2007, Trends in biotechnology.

[28]  Martyn C. Davies,et al.  Comparison of calibration methods for atomic-force microscopy cantilevers , 2002 .

[29]  N. Gavara,et al.  Probing mechanical properties of living cells by atomic force microscopy with blunted pyramidal cantilever tips. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  J. Käs,et al.  The optical stretcher: a novel laser tool to micromanipulate cells. , 2001, Biophysical journal.

[31]  James R Friend,et al.  Spring constant calibration of atomic force microscope cantilevers of arbitrary shape. , 2012, The Review of scientific instruments.

[32]  Paul Mulvaney,et al.  A virtual instrument to standardise the calibration of atomic force microscope cantilevers. , 2016, The Review of scientific instruments.

[33]  John E. Sader,et al.  Parallel beam approximation for V‐shaped atomic force microscope cantilevers , 1995 .

[34]  Chwee Teck Lim,et al.  Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria. , 2005, Acta biomaterialia.

[35]  M. Lekka,et al.  Cancer cell recognition--mechanical phenotype. , 2012, Micron.

[36]  E. Elson,et al.  Cellular mechanics as an indicator of cytoskeletal structure and function. , 1988, Annual review of biophysics and biophysical chemistry.

[37]  R. Hochmuth,et al.  Micropipette aspiration of living cells. , 2000, Journal of biomechanics.

[38]  Daniel Isabey,et al.  Assessment of mechanical properties of adherent living cells by bead micromanipulation: comparison of magnetic twisting cytometry vs optical tweezers. , 2002, Journal of biomechanical engineering.

[39]  I. N. Sneddon.  The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary profile , 1965 .

[40]  Daniel J Müller,et al.  Atomic force microscopy as a multifunctional molecular toolbox in nanobiotechnology. , 2008, Nature nanotechnology.

[41]  J. Sader,et al.  Frequency modulation atomic force microscopy reveals individual intermediates associated with each unfolded I27 titin domain. , 2006, Biophysical journal.

[42]  P. Janmey,et al.  Tissue Cells Feel and Respond to the Stiffness of Their Substrate , 2005, Science.

[43]  J. Sader,et al.  Method for the calibration of atomic force microscope cantilevers , 1995 .

[44]  Mark A. Wendman,et al.  Micromachining and Imaging , 1997 .

[45]  R. Proksch,et al.  Noninvasive determination of optical lever sensitivity in atomic force microscopy , 2006 .

[46]  Arvind Raman,et al.  Equivalent point-mass models of continuous atomic force microscope probes , 2007 .

[47]  Benjamin Ohler,et al.  Cantilever spring constant calibration using laser Doppler vibrometry. , 2007, The Review of scientific instruments.

[48]  S. Chizhik,et al.  Atomic force microscopy probing of cell elasticity. , 2007, Micron.

[49]  P. Hansma,et al.  A nondestructive method for determining the spring constant of cantilevers for scanning force microscopy , 1993 .

[50]  Giovanni Dietler,et al.  Gradient of rigidity in the lamellipodia of migrating cells revealed by atomic force microscopy. , 2005, Biophysical journal.

[51]  S. Silbernagl,et al.  Characterization of two MDCK-cell subtypes as a model system to study principal cell and intercalated cell properties , 1994, Pflügers Archiv.

[52]  Thorsten Hugel,et al.  Atomic force microscopy spring constant determination in viscous liquids. , 2009, The Review of scientific instruments.

[53]  Vera C. Fonseca,et al.  Cellular mechanical properties reflect the differentiation potential of adipose-derived mesenchymal stem cells , 2012, Proceedings of the National Academy of Sciences.

[54]  Gerber,et al.  Atomic force microscope. , 1986, Physical review letters.

[55]  H. Hertz.  Ueber die Berührung fester elastischer Körper. , 1882 .

[56]  J. Kramar,et al.  Atomic Force Microscope Cantilever Flexural Stiffness Calibration: Toward a Standard Traceable Method , 2011, Journal of research of the National Institute of Standards and Technology.

[57]  Teodor Gotszalk,et al.  Calibration of atomic force microscope , 2008 .

[58]  F. Yin,et al.  Assessing Micromechanical Properties of Cells with Atomic Force Microscopy: Importance of the Contact Point , 2007, Biomechanics and modeling in mechanobiology.

[59]  P. Milani,et al.  Adhesive-free colloidal probes for nanoscale force measurements: production and characterization. , 2011, The Review of scientific instruments.

[60]  C. Rotsch,et al.  Dimensional and mechanical dynamics of active and stable edges in motile fibroblasts investigated by using atomic force microscopy. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[61]  Manfred Radmacher,et al.  Studying the mechanics of cellular processes by atomic force microscopy. , 2007, Methods in cell biology.

[62]  Richard S Gates,et al.  Precise atomic force microscope cantilever spring constant calibration using a reference cantilever array. , 2007, The Review of scientific instruments.