(18h) Migratory Single Cell Force Measurements Using Deformable Suspended Nanofiber Networks

Introduction

During migration,
cells exert forces in their immediate microenvironment known as the
extracellular matrix (ECM), a nanofibrous mesh which provides geometrical and
chemical cues that directly affect cell behavior¹.  While the nature and magnitude of these forces are dependent on the ECM itself, they can also reveal important information about the mechanical state of the cell².  For instance, recent works have demonstrated that traction forces can be directly related to cellular differentiation, and cancer progression has also been shown to have an effect on the cell's mechanical state, thereby altering contractility^3,4.  Many recent efforts have been devoted to measuring cell traction and migration forces using micropost arrays and deformable gel surfaces, which are unable to capture entire 3D effects on force generation^3,5,6. Therefore, there is clearly both great interest and need for the ability to quantify the forces a cell exerts on the ECM using a system which allows cells to migrate along 3D geometries mimicking ECM mechanical environments.  In this work, we present a method to measure real-time migration forces of single cells using a system of suspended nanofiber beams whose stiffness (N/m) is readily adjustable.  As cells attach and begin moving along these scaffolds, individual fibers with clamped boundary conditions deflect in the elastic limit, allowing cell migration forces to be calculated via classical beam theory.  With this technology, cells may be monitored in real-time for the forces they exert on their ECM-mimicking environment.  Implications of this work include understanding internal cell forces during differentiation and therefore the future design of accurate tissue engineering scaffolds, drug testing platforms, and identification of diseased cells including cancer.

Materials and Methods

            Scaffolds were fabricated
using the previously reported STEP (Spinneret-based Tunable Engineered
Parameters) platform, a non-electrospinning fiber manufacturing technique^7?10.  Briefly, polymer solution is injected through a microneedle and a rotating substrate is brought into contact with the resulting droplet.  As a controlled stage translates the hollow scaffold, aligned fibers are deposited on hollow substrates in criss-cross layers which were fused at intersections forming nanonet structures. 

            After creating the
scaffolds, C2C12 mouse myoblasts were seeded onto the STEP scaffolds and
attached within 4-6 hours. Cells then began migrating along the structures.  .Migration
was visualized via time-lapse videography using an incubating microscope with a
digital three-axis stage (Zeiss).  Images were taken every 10 minutes for 12
hours, which captured cells deflecting STEP fibers.  Built-in software allowed
measurements to be taken relevant to calculating forces including fiber length,
positioning of the load, and deflection distance.

            Cells were assumed to
cause deformation to the nanofibers according to classical beam theory with
clamped-clamped boundary conditions in the elastic limit, described by the
following equation:

where ?P' is the applied load to
fiber length ?L' at distance from the boundary ?a'.  The elastic modulus ?E' is
a material dependent parameter, and the moment of inertia ?I' is shape
dependent.  Therefore, as a deflection ?d' is noted, the applied load may
be calculated.  Forces were assumed to be applied as a single load perpendicular
to the point of maximum deflection, an assumption that will be further
investigated in the future.

Results and Discussion

After spinning
two layers of fibers on the STEP scaffolds, fiber intersections were fused together
(Fig. 1a).  As shown in Fig. 1b, the resulting grid-like nanostructure can be
considered as a system of springs with individual fiber stiffnesses (N/m) being
dependent on the fiber material, diameter, and length as well as positioning
along the fiber.  Designing a scaffold in which the longitudinal fibers are
stiffer than the latitudinal fibers results in a system in which the less stiff
fibers deflect while the larger fibers can be considered immobile. 

https://proceedings.aiche.org/sites/default/files/aiche-proceedings/con…" height="307" class="documentimage">

Cells were found
to attach to the scaffolds and began migrating along the suspended fibers.  As
cells attached to both the stiffer and less stiff fibers simultaneously, the
less stiff fibers deflected under forces exerted by the cells (Fig. 2).  These
deflections were measured and then calculated using the aforementioned equation
to obtain migratory cell forces in a natural 3D fibrous microenvironment. 

https://proceedings.aiche.org/sites/default/files/aiche-proceedings/con…" height="275" class="documentimage">

Figure 2 shows
an example timelapse of a C2C12 mouse myoblast migrating and deflecting a
horizontal fiber.  In this 30 minute sequence, the cell progresses along both
fiber axes, causing the cell to stretch further and further apart.  Using frame
C as an example calculation, a PS fiber of d=500 nm diameter spanning L=100 μm, pulled a=55μm from the boundary
would require an 18 nN force to deflect a distance of d=10μm.  This is in good
agreement with other force measurement systems, which often predict migratory
forces ranging from tens to hundreds of nN¹¹.  While this does not necessarily represent the maximum force that a C2C12 is able to exert, it does show what the cell was experiencing during that stretching phase. 

https://proceedings.aiche.org/sites/default/files/aiche-proceedings/con…" height="298" class="documentimage">

In addition to
testing normal cell lines, DBTRG (Denver Brain Tumor Research Group) cells were
also examined.  These cancerous cells, which originate from an aggressive brain
cancer called glioblastoma multiforme, were also seeded onto the STEP scaffolds
for force evaluation (Fig. 3).  Again, as an example calculation using the
above timelapse in frame C, a PS fiber d=500 nm in diameter spanning L=108 μm, pulled a=28 μm from the boundary
would require a 23 nN force to deflect a distance of d=7.5 μm.  As more cells are
evaluated in each condition, we will be able to distinguish weather or not the
cancerous state of a cell changes its migratory forces.

Conclusions

            We have
presented a method which for the first time measures real-time migratory forces
of single cells using fused, suspended nanofibers.  This system is advantageous
in that it accounts for 3D topographies that would be experienced by cells in
vivo.  With this method, migration forces have been measured in the 10-100
nN range, but more or less sensitive structures may be developed simply by
adjusting the stiffness of the fibers which makeup the scaffold.  Decoupling
force vectors from attached cells remains a challenge and will continue to be
investigated in the future.  In addition to gathering additional data for
cancerous and non-cancerous cell lines to determine a baseline migratory force
value for each case, this system will be used to simultaneously evaluate migratory
forces and associated differentiation of stem cells in future work. 

References

(1) Lock, J. G.; Wehrle-Haller, B.; Strömblad, S. Seminars
in cancer biology 2008, 18, 65-76.

(2) Crow,
A.; Webster, K. D.; Hohlfeld, E.; Ng, W. P.; Geissler, P.; Fletcher, D. A. Biophysical
Journal 2012, 102, 443-451.

(3) Fu,
J.; Wang, Y.-K.; Yang, M. T.; Desai, R. a; Yu, X.; Liu, Z.; Chen, C. S. Nature
Methods 2010, 7, 733-736.

(4) Ketene,
A. N.; Schmelz, E. M.; Roberts, P. C.; Agah, M. Nanomedicine :
nanotechnology, biology, and medicine 2011, 8, 93-102.

(5) Ricart,
B. G.; Yang, M. T.; Hunter, C. a; Chen, C. S.; Hammer, D. a Biophysical
journal 2011, 101, 2620-8.

(6) Rape,
A. D.; Guo, W.-H.; Wang, Y.-L. Biomaterials 2011, 32,
2043-51.

(7) Ker,
E. D. F.; Nain, A. S.; Weiss, L. E.; Wang, J.; Suhan, J.; Amon, C. H.;
Campbell, P. G. Biomaterials 2011, 32, 8097-107.

(8) Nain,
A. S.; Phillippi, J. a; Sitti, M.; Mackrell, J.; Campbell, P. G.; Amon, C. Small
(Weinheim an der Bergstrasse, Germany) 2008, 4, 1153-9.

(9) Bakhru,
S.; Nain, A. S.; Highley, C.; Wang, J.; Campbell, P.; Amon, C.; Zappe, S. Integrative
biology : quantitative biosciences from nano to macro 2011, 3,
1207-14.

(10)      Nain,
A. S.; Sitti, M.; Jacobson, A.; Kowalewski, T.; Amon, C. Macromolecular
rapid communications 2009, 30, 1406-12.

(11)      Ferrell,
N.; Woodard, J.; Hansford, D. J. Sensors and Actuators A: Physical 2011,
170, 84-89.