Microrheology of Biopolymers at Non-thermal Regimes - Tissue Engineering: Computer Modeling, Biofabrication and Cell Behavior - page 96

using MLO-Y4 cells) and correlated these with their ability to release nitric oxide in
response to minute stresses; we showed that cell shape directly correlated with the
measured elastic modulus and mechanosensitivity [ 3 ], supporting the notion that
physical parameters drive biologically relevant functions [ 4 - 7 ]. However, the un-
derlying biophysical events are not well understood. Among several hypotheses,
one may associate molecule-level deformation of trans-membrane proteins on cell
membranes as triggering event to initiate relevant biochemical cascades directly af-
fecting cell behavior [ 4 , 8 , 9 ]. Although promising, corresponding models for com-
plex molecule deformation is still lacking. An approach based on approximating
molecules as elastic rods are particularly successful in assessing high frequency fluc-
tuations of biopolymers (at thermal equilibrium) [ 10 - 14 ]. However, biopolymers
have complex structures [ 15 - 17 ], which have unknown coupling to their mechani-
cal properties, and trans-membrane proteins are subjected to non-thermal forces at
the onset of mechanosensing. Therefore, to develop a generic and robust approach,
this study aims to design experimental and analytical methods for quantifying heli-
cal biopolymer deformation, since the helix is a basic structure from which higher
orders of structure could be based.
A simple molecular geometry with sufficient complexity is that of a helix. Deo-
xyribonucleic acid, or DNA follows a helical structure and under right conditions
form higher order coils that may appear globular. Actin, one of the cytoskeletal pro-
teins, is also a helix, whereas collagen, a common tissue biopolymer is a triple helix
[ 15 , 16 ]. A previous study from Bernido and Carpio-Bernido 2005 showed that pro-
tein folding can be characterized using winding probabilities associated with the
number of turns and the resulting length of the biopolymer under the appropriate
strain [ 18 , 19 ]. This approach is here adapted and will be investigated for charac-
terizing biopolymer tension based on the unwinding of its helical structure under
pre-defined tension.
A robust experimental tool for measuring the mechanical properties of molecules
to living cells uses colloidal particles as probes. The Brownian motion of an em-
bedded probe could be used to infer the complex shear modulus to quantify bulk
mechanical properties of soft materials (e.g., a living mammalian cell) [ 11 , 20 - 22 ].
In single biopolymers, the fluctuation spectra of an attached probe contain enough
information to quantify mechanical properties. A low-cost optical trap system can
be implemented in microscopes (in bright field or differential interference contrast
mode) to manipulate and monitor the Brownian motion of optically confined probes
for one-particle or two-point passive microrheology [ 3 , 20 , 21 , 23 - 25 ]. Active mi-
crorheology is however implemented by measuring the mechanical responses to
stimulation by wiggling a trapped embedded probe at known oscillations.
2 The Winding Probability Function
Depending on a single biopolymer's stiffness, its mechanical properties can be
fully described based on a few parameters. For example, very compliant polymers