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Active Computational Modelling of Cytoskeletal Remodeling During
Compression and Spreading
Ronan, W. 1 , Deshpande, V. S. 2 , McMeeking, R. M. 3 , McGarry, J.P. 1
1 Department of Mechanical and Biomedical Engineering, National University of Ireland, Galway
2 Department of Engineering, University of Cambridge
3 Department of Mechanical Engineering, University of California, Santa Barbara
email: w.ronan1@nuigalway.ie
Abstract
Cell spreading is governed by two cooperative
cellular processes: the formation of focal adhesions,
and the active remodeling of the actin cytoskeleton as
the cell spreads 1 . The interaction between these two
processes is poorly understood, and previous
computational models have only examined each process
in isolation. We demonstrate that a novel formulation
that captures key biochemical processes can accurately
capture experimentally observed measurements.
1. Introduction
In the present study an active constitutive
formulation for the remodelling and contractile
behaviour of the actin cytoskeleton and focal
adhesions 3,4 is used to simulate cell spreading on a flat
substrate. Additionally this modelling framework is
used to predict the response of round and spread cells to
compression.
2. Materials and methods
The actin-myosin cytoskeleton is formed via the
assembly of myosin and actin filaments into contractile
stress fibre (SF) bundles. This is captured in our
constitutive model by allowing SFs to assemble in any
direction at any point in the cell. The contractile
behavior of SFs due to the cross-bridge cycling of the
actin-myosin pairs is described by a Hill like equation:
The signal induced formation and tension dependent
dissociation of the actin cytoskeleton is captured using a
first order kinetic equation. This equation gives the
dimensionless activation level of a SF bundle, η,
where C is an exponentially decaying signal. This
formulation has been implemented in a finite element
user-defined material. A model that accounts for the
mechano-sensitivity of focal adhesions based on
thermodynamic considerations is coupled with an
exponential cohesive zone model to simulate spreading.
3. Results
SF evolution during spreading is shown after 5 mins
and after 25 mins in Fig. 1A. SFs form at the base of the
cell and form distinct bundles leading over the nucleus.
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A band of stress fibres also forms at the periphery of the
cell. Focal adhesions are predicted to cluster at the outer
edge of the cell.
Compression of round (Fig. 1B) and highly spread
(Fig. 1C) cells is also simulated. Significantly more SF
are computed in spread cells prior to compression.
Following compression to 70%, compression forces for
the active model show very good agreement with
experimental data 2 , with the spread cell requiring 6
times more force. In contrast, using a hyperelastic
material only gives a 1.5 fold increase (Fig. 1D)
Figure 1 SF evolution in a spreading cell after 5min
and 25min (A), and in cells before compression
(C&D). Compression forces for cells using passive
& active models and experimental 2 data.
4. Discussion
The model presented here predicts the development
of SFs during active spreading similar to experimentally
observed behaviour. Spread cells are shown to have
more SFs than round cells. This causes the higher
compression forces observed experimentally, which
have been captured by our model. Traditional cell
models cannot capture these phenomena and therefore it
is essential to include the active remodelling of the
cytoskeleton in numerical models.
5. References & acknowledgements
[1] Guilak et al., J. Biomech 33:1663-1673, 2000.
[2] Caille et al., Biomech 35:177-187, 2002.
[3] Deshpande et al, PNAS 463:787-815, 2007.
[4] Deshpande et al, JMPS 56 (4), 1484-1510, 2008.
SFI-(08/RFP/ENM1726), IRCSET, ICHEC