Biomechanics, as a bridge between physical
and biological sciences, has emerged greatly in the last decades. It
demonstrated the potentials of interdisciplinary sciences bringing fundamental knowledge
in the topics of macroscopic mechanics dealing with the function and movement
of the body and the dynamics of blood flow. As the technology developed more
and more devices became available for studying mechanical properties at
cellular and molecular level, allowing sub-nanometer scale spatial and piconewton
scale force resolution measurements.

Consequently,
more and more novel knowledge started to be gatherd about the mechanical
properties of the cell, how big forces a cell can exerts on its environment,
what are the elastic properties of a cell, is it different between cell types
and is it changing if the cell get sick (by bacteria (malaria), or cancer), and
how about the molecules (unbinding forces, the pushing force of microtubule polymerization).
A new research field started to be formed and called (used) as
nano-biomechanics.

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This growing number of methods and
investigations with the aim to elucidate the principles of life-supporting
molecular and cellular interactions started to form nano-biomechanics, a new
research field merging together the topics of mechanics, engineering, biology
and medicine.  

magnetic
twisting cytometry12, micropipette aspiration 13, cell poker 14 or
scanning acoustic microscopy 15. micropipette aspiration (typical force
range, 1–100 nN)

The tools of this cross-field is wide, containing
several novel and reconsidered approaches, such as….., however, the main toolset consist of
AFM, magnetic tweezer, optical tweezer-stretcher and cell traction force
microscopy. Optical and magnetic tweezers are particularly useful to analyze cellular interactions
at a single-molecule resolution. Despite the high force sensitivity the
maximal adhesion forces that laser tweezers can measure is limited (usually
below 100 pN).  With x it was demonstrated that…., while y was
used to measure …, but z,v,w were also applied to reveal important questions
about… X is mostly used for …. With the help of it xxx could be measured
(demonstrated, obtained). Y is very efficient in measuring forces at pN scale,
but the upper range is limited at 100 pN. Bla and bla was obtain with. Among
these, AFM is maybe the most versatile and outstanding system serving as a
reliable and accurate nanoforce tool. It offers the largest range of detectable
forces (from 10 pN up to 1000 nN), precise spatial (~1 nm to ~100 µm) and temporal
(~0.1
s to > 10 min) control, the relatively simple use and the allowance of measurements
is physiological environment.

1. Atomic
force microscopy as a tool of nano-biomechanics

Atomic force microscope (AFM) is a non-optic
microscopy technique developed in the 80’s by Binnig, Quate and Gerber as part
of the scanning probe microscope superfamily 1. Although strong developments have taken place since then, the main
concept is still the same, where a sharp probe is taken in close proximity to
the sample and scans its surface driven by different feedback methods to build
up a highly resolved three-dimensional topographic image. This relatively
simple working principle of the instrument gave the possibility to a fast
development and resulting in capabilities such as imaging structures from
tissue to single molecules 2,3, scanning with video rate speed 4, or measuring forces on the pN scale 5.

The vital part of the AFM is a very flexible
cantilever containing an extremely sharp micro fabricated tip that deflects
when interacting with the sample surface. The optical lever method is the most
used approach to detect the slight deflection changes of the cantilever and to
provide a constant feedback keeping the tip in the near-field of the sample.
Principally it uses a focused laser beam reflected from the backside of the cantilever
that falls on a quadrant photodiode. 
Hence, the slight bending of the cantilever causes enhanced spatial
variations of the laser spot on the detector that can be precisely determined.

Apart from its high resolution imaging
capacity the AFM holds several other advantages. It provides a
three-dimensional surface profile, requires minimal sample preparation and can
be easily combined with optical microscopy or other spectroscopy techniques,
like Raman or IR 6,7. The presence of a physical probe in close proximity to the sample
allows exploring a wide variety of physico-chemical properties. Hence, AFM can
provide quantitative data together with surface topography about the sample’s
elasticity 8, friction 9, or adhesion forces 10. In addition, maybe its most important capability in respect to life
sciences is to perform measurements under physiologically relevant conditions.

1.1. Force
measurements: force distance curve  

Although atomic force microscopy (AFM) was
first utilized in biology as a surface imaging technique, soon after its
invention researchers have applied it to study the mechanical properties of
living cells and other biological samples by force spectroscopy 11. During force spectroscopy measurements the horizontal (x,y)
position of the cantilever is fixed and its vertical movement (z) and
instantaneous deflection, in response to various forces, are recorded in a
series of so called force-distance curves (FD-curves) in a cyclic manner.

Figure 1 depicts
a representative FD-curve. The force cycle starts at several micrometers far
from the surface (A). The cantilever with a constant velocity approaches the
sample, reaches the surface (B) and starts to deflect until its deflection will
correspond to the preset trigger force (C). Following a certain contact time
the cantilever is withdrawn. If adhesion is present the forces required to
detach the probe from the investigated surface will deflect the cantilever in
the negative direction. The strength, length and number of individual bindings will
alter the shape of the retraction part of the curve that serves as a
fingerprint of the probe-sample interaction. After the probe have reached large
enough distances where all interaction forces cease the cycle finishes. The resulted
FD-curves are the raw data of fore spectroscopy measurements that allows the
extraction of various parameters belonging to the mechanical properties of the
sample or related to the interactions between the substrate and the probe. By
fitting the approaching (red) part of the FD curve with different theoretical
models the Young’s modulus of the sample can be obtained. The force difference
between the starting and minimum points gives the maximal adhesion. This is
composed by individual ruptures (close-up) whose number, step-size, but even
their occurrence distances are important parameters of the interaction. Besides
these, several type of works can be extracted, such as work of de-adhesion,
total work used to bend the cantilever, but also the dissipated (or plastic)
work during the cycle and the elastic work exerted by the sample to recover the
initial shape. By quantifying these parameters a mechanical phenotype of the
sample (tissue, cell) can be determined that is well defined for different type
of cells, and tissues (ref??).

1.2. Elastic
modulus determination

Living cells are continuously perceiving,
processing and responding to mechanical signals received from their
surroundings. Elastic properties are determining for cells in order to perform
their role properly. AFM based nanoindentation measurements has provided
valuable data about the elastic modulus of various living cell cultures. The
obtained values vary over wide range from 0.1 up to 100 kPa, depending on cell
type, sample preparation, indentation depth and the used calculation model 12,13. Evidently, cytoskeleton is dominant in determining cell stiffness,
as several studies have demonstrated, however, the different cytoskeletal components
contribute with varying degrees. While cytoskeleton F-actin depolymerization by
cytochalasin D resulted a reduced cell stiffness, showing the crucial role of
the F-actin network 14, studies on microtubule depolymerization obtained little effect on
cell membrane mechanical resistance 15.

To quantify the elastic (or Young’s) modulus of
the sample the data points at the contact region of FD-curves must be fitted with
theoretical models, of which the Hertz-Sneddon model is the most widely used. The
problem of contact between a rigid spherical probe and an elastic half-space
was first solved by Hertz 16 that was further developed by Sneddon for different tip shapes 17,18. The relation between loading force (F) and indentation depth (?) for a conical hard indenter is the following:

                                                                                                 (1)

Here, E is the Young’s modulus, ? is the half-angle opening angle of the cone, while ? denotes the sample’s Poisson ratio. Despite its simplistic assumptions, provided
that adhesion forces are much smaller than the maximum force-load and indentation
depths are less than 10% of cell thickness Hertz-Sneddon model is applicable 13,19.

1.3. Force
mapping

Thanks to the precise positioning
capabilities of the AFM, an elegant way of data acquisition is defining a grid
over a selected area of the sample and performing force measurements in every
grid nodes. This enables to study the spatial distribution of mechanical
properties over entire tissues, cells or sub-cellular structures. The result is
a set of data which contains not only morphological information, but can be spatially
correlated with the various parameters extracted from the individual FD-curves.
By this several maps can be reconstructed about the selected area, each showing
the different spatially resolved physico-chemical properties (see figure x and
figure y in chapters w and v respectively).

1.4. Single
cell force spectroscopy

Cells are in continuous communication with
their environment by means of a constant exchange of physical and biochemical
signals. Apart from their fundamental role in the development and maintenance
of tissues, cell adhesion forces are essential in stimulating signaling
pathways that regulate important cellular processes, such as migration,
proliferation, survival, and differentiation 20. AFM was proven to be a versatile tool to quantify a wide range of
adhesion forces at physiological conditions. Although, in usual force
measurements the probe is a stiff material, usually made out of silicon or
silicon nitride, several biological objects could serve as a probe. The AFM tip
can be functionalized with various molecules for specific intermolecular
binding measurements 21, or with bacteria for testing its adhesion to different substrates 22, but even  whole living cells
can be immobilized on the cantilever and used as a probe. The latter case is
called as single-cell force spectroscopy (SCFS) 23,24. This method has the exceptional ability to directly quantify
interaction forces between two living cell down to the contribution of single
molecules.