PHYSICAL REVIEW LETTERS

1
Cooperativity between Cell Contractility and
Adhesion

• PHYSICAL REVIEW LETTERS
• Igor L. Novak, Boris M. Slepchenko, Alex
  Mogilner, and Leslie M. Loew
• Presented by
• Aabid Shariff
• Joint CMU-Pitt Program in Computational Biology
• University of Pittsburgh School of Medicine

2
Contents

• Background
• Movement of cells
• Hypothesis
• Modeling
• Equations describing phenomena
• Analysis
• Steady State
• 1D, 2D, 3D solutions
• Conclusions

3
Cell Movement
Tilghman RW, 2005
4
Focal Adhesions and Stress Fibers
5
Hypothesis
6
Equations based on mass conservation
Non-dimensionalizing..
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Steady State Analysis

• Self-induced force field, E
• Convex function, phi
• Gradient of phi
• 1D case Stress Fibers create a force that is
  increasing from the a minimum point inside the
  cell to the exterior of the cell.
• Introduction of M

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Final Equation in 1D case
Beta is a measure of the ratio of the
dissociation to association
Patterns of steady state adhesion distribution
There is bistability active, inactive for beta
lt 1/8. Experiments confirm this when stress
fibers are inhibited.
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Numerical solution of 1D Eqs.
Red free integrin molecules Blue adhesion
molecules

• Splits due to zero net force at the midpoint
• The force is due to the formation of stress fibers

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Understanding Time Scales
For slow diffusion,
In diffusion limited case, v is prop to
D Integrins are released from the rear of the
peak and can travel only if there is a certain
threshold of free integrins. Fire-diffuse-fire.
Hence, we have a threshold diffusion length and
we have an effective diffusion coefficient.
Overall time scale is in hours, just like in
experiments.
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Experiment and simulation of the pattern of cell
adhesion on a square substrate the 2D case

• focal adhesions relocate to the cell periphery
  and concentrate at the corners
• This is because the net force at the center of
  the square is small unlike at the ends.
• Basic Idea - at the high-curvature regions, the
  sum of unit vectors directed along stress fibers
  is amplified.

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Adhesion Density vs Curvature
Steady-state distribution of adhesions
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• Conclusions
• More curvature, more accumulation of adhesion
  molecules. Hence the non-uniform distribution.
• This is explained by the positive feedback
  between stress fibers and adhesion.
• Model correctly predicts redistribution of
  adhesions with time scale as hours.