Dynamics of Active Cellular Response under Mechanical Stress

1
Dynamics of Active Cellular Response under
Mechanical Stress

• Rumi De
• Division of Engineering
• Brown University

Collaborators Theory

Samuel A. Safran (Weizmann Institute of
Science, Israel) Assaf Zemel (Hebrew
University, Israel)
Expt R. Kemkemer (Stuttgurt, Germany) S.
Jungbauer (Stuttgurt, Germany) J. Spatz
(Stuttgurt, Germany)
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Cell Physics Motivations

• cells exert forces on medium

• Cell activities - spreading, differentiation
  depends on mechanical environment

100mm
(Harris et.al. 1980)
Differentiation of stem cells
Mechanical environment of cells
(Engler, Sen, Sweeney, Discher, Cell, 2006)
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Cells Align Perpendicular to Cyclic Stretching
Rat Embryonic Fibroblasts REF52wt (Connective
Tissue Cells)
Expts S. Jungbauer, R. Kemkemer et. al.
Frequency 1Hz Amplitude 8 Stopped after
30000 sec Further Recording 30000 sec
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Cellular Orientation Static Vs Cyclic Strain
static - parallel
(Eastwood et.al. 1998 time one hour fibroblasts)
a puzzle over many years
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Outline of the talk

• Cell orientation response - dynamical puzzle
• Cell response to stress or strain
• Cell orientaion competing random forces
• Relaxation time to reach to the steady state
  orientation

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Cell mechanosensitivity adhesion dependent
focal adhesions
stress fibers
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Our Model
cells internal activity mechanical force
exerted by the matrix
state of the cell contractile activity
and cellular orientation
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Theory Cell force dipole
microscopic
mesoscopic force dipole
Balaban et al. Nature Cell Biol. 2001 Schwarz et.
al. Biophys J. (2002)
force dipole
P lt 0 contractile
(Schwarz, Safran, PRL 2002 Bischofs, Safran,
Schwarz, PRE 2004.)
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Internal cellular activity
force dipole
Experiments
P
matrix reaction stress R,
(Tan et.al. PNAS, 2003)
(Elastic Greens function relates strains to force
dipole)
Cell mechanosensor and activity set point stress
P
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cell activity dipole reacts to local stress
In presence of external stress
total local stress along Z

• Cell mechanosensor and activity
• set point stress P

P
5 10 15
2 0 Time
(min)
(Tan et.al. 2003)
R. De, A. Zemel, S. Safran Nature Physics
(2007)
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Cell reaction to matrix forces
Deformation energy due to force dipole
(E - Elastic modulus) Dipole energy in external
strain field
(contractile dipole P lt 0 tensile
stress uijgt0 )
(calculations elastic Greens functions)
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Dynamics external stress
Total effective free energy
Relaxation dynamics

• Theory parameter cell force c
• Experiment controls External stress Pa
  frequency wa,
• Youngs modulus E.
• tP time scale of molecular reorganization of
  cytoskeletal
• tq longer time scale for the cooperative
• reorientation of the cytoskeleton
• P set point stress
• - measure w/o external stress

P
5 10 15
20 Time (min)
(Tan et.al. 2003)
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Steady State Orientation

• Static stress field Pa time independent

optimal orientation - parallel

• Dynamic stress field

T Pa 1 cos (w t)
If 1/ w ltlt readjustment time of focal adhesions
Long time solution average free energy over a
cycle

• Threshold cyclic stress for perpendicular
  orientation
• - 1-4 (Wang, Dartsch, Kemkemer groups)

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Cell orientation as a function of frequency
blue rigid matrix red soft matrix

• Physics frustration of cell forces in dynamical
  case

De, Zemel, Safran, Nature Physics (2007) De
Safran, PRE (2008)
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Cell response stress or strain ?
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Does cell feel stress or strain ?
constant deformation?
(Saez et. al, Biophys J.2005)
constant force?
(Freyman et. al, Expt. Cell , 2005)
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Cell orientation stress or strain
Dynamic stress field T Pa 1 cos (w t)
If 1/ w ltlt readjustment time of focal
adhesions, orientation,
Long time solution average free energy over a
cycle
optimal strain
cell orients in direction of minimal strain -  
Poissons ration
optimal stress
cell orients in direction of minimal stress -  

• A possible way to identify the controlling factor
  as stress or strain

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Poissons ratio dependence of orientation
optimal strain
optimal stress
blue --gtred --gt black --gt increasing matrix
forces

• Tool to identify the controlling factor as stress
  or strain

R. De, A. Zemel, S. Safran Biophys J. Lett.
(2008).
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Random Cellular Orientation
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Experiments random cell alignment
No external stress
(Wang et.al. 1998 endothelial cells)
quasi-static external stress
Expt fibroblasts
Jungbauer, Gao, Spatz Kemkemer, BioPhys. J.
2008
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Model competing random forces
Effective tempetarure stochasticity involves in
cellular procesess
assume Boltzmann-distribution probability
(Kemkemer et al., Eur. Phys. J. ,2000 Jakab et
al., PNAS ,2004)
f scaled average free energy over a cycle Ts
scaled effective temperature
Increasing Ts
solid line high temperature dashed low
temperature
If effective temperature low enough cell orients
parallel to quasi-static stress - for
intermediate temperature cells align randomly
to quasi-static stress
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Frequence Dependence Relaxation Time
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Orientational relaxation time Vs. frequency
Theory
Expt
Relaxation time scale
where steady state orientation
at low frequency, t increases with 1/w2
(Jungbauer, Gao, Spatz Kemkemer, BioPhys. J.
2008)
at high frequency,
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Summary and outlook

• Theory parameter cell force, c
• Experiment controls external stress, Pa ,
  frequency, w, Elastic modulas E
• Several predictions
• - static applied stress parallel
• - high frequencydynamic stress
  perpendicular
• - distribution of angles thermal, internal
• - non-linear response
• - threshold stress

• A possible  way to identify the controlling
  factor of cell activity
• - stress fixed point cell orients
  perpendicular
• - strain fixed point zero strain direction

• Frequency dependence of the relaxation time

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Thank you
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Average Free Energy
f scaled average free energy over a cycle Ts
scaled effective temperature