A Viscoelastic Model to Explore Force Mechanotransduction within the Focal Adhesion Complex

1
A Viscoelastic Model to Explore Force
Mechanotransduction within the Focal Adhesion
Complex

• Ricardo R. Brau
• Nicholas A. Marcantonio
• BE. 400 Project
• December 11, 2002

2
Overview

• Motivation
• Mathematical Model
• Model Results
• Proposed Experiments
• Conclusion

3
Motivation Signal Transduction or Transmission

• External forces Important in Development
  ?induction of biological responses in cells
  (apoptosis, differentiation, etc.)
• Interface between mechanics and biochemistry must
  be explored
• Localized Model vs. Decentralized Model for
  Mechanotransduction

• Want to use model to examine localization of
  deformation in FAC
• Explore potential for signal transduction due to
  molecular deformation in FAC vs. cytoskeleton

Krammer et al, 1999 Shafrir and Forgacs, 2001
Bao, 2002
4
Deformations of Single Molecules

• Most experimentation performed on rodlike
  molecules (DNA/RNA and titin), molecular motors
  (kinesin and myosin), and fibronectin

Kellermayer et al, 1999
5
The Focal Adhesion Site
Zamir and Geiger, 2001
6
Model System
Applied Force

• FAC is highly dynamic, and not well characterized
• Want to start with simple model

Membrane
ß
a
aalpha ?beta Ppaxillin Ttalin Vvinculin Aact
in
P
T
V
A
Zamir and Geiger, 2001
7
Mechanical Deformations in Biology

• Assume m0
• ? controls kinetics
• k affects steady-state and kinetics

• Model molecules as viscoelastic elements

Bao, 2002
8
Model Assumptions

• Deformation, not relative molecular position,
  determines signaling
• Relative deformation ?x
• Strain ?x/L
• FAC structure is time-invariant
• Signaling due to molecular deformation, not
  disruptions in FAC structure
• 2o and 3o structures preserved
• hinge motion between molecules not significant
• Molecules can be represented as single domains

Subbiah, 1996 Oberhauser et al, 1998 Idiris et
al, 2000
9
Viscoelastic Model of the FAC
10
Mathematical Model

• 6 unknowns and 6 equations

(1) (2) (3) (4) (5) (6)
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Mathematical Model

• Solve numerically using MATLAB ode23s
• Initial condition system is at rest

FForcing Matrix SSpring Matrix DDamping
Matrix
12
Parameter Estimation

• Molecular breathing due to thermal forces 1pN
• Domain unfolding 100 pN
• Deformation length scales 0.05-5 nm
• Deformation time scales 10 nsec
• Only actin well characterized as mechanical
  element
• Only molecular weight information available for
  other molecules

Marszalek et al, 1999 Zhu et al, 2000 Craig et
al, 2001 Bao, 2002
13
Parameter Estimation

• Hydrodynamic radius model molecules as spheres
• Since ? only affects kinetics, assume similar for
  all molecules 60 pN sec/m
• k .02 nN/nm for 172 kDa molecule, consider
  proportional to molecular weight
• Signaling occurs at arbitrary threshold of 10
  strain

Fisher et al, 1999 Bao, 2002,
14
Parameter Estimation

• Scenario 1
• Each protein has same spring constant
• Length is calculated as a function of MW
  (hydrodynamic radius)
• Measure strain (?x/L)
• ?x will be the same for each protein, but strain
  will be different

• Scenario 2
• Each protein has the same length
• k is proportional to MW
• Based on k.02 N/m for MW of 172 kDa
• Measure strain (?x/L)
• L will be the same for each protein, but ?x will
  be different

• Perform simulations for static and dynamic loading

15
Model Results

• Static Force 4 pN (thermal force)

16
Model Results (cont.)
17
Model Results (cont.)
18
Model Results (cont.)
19
Model Results (cont.)
20
Experimentation/Model Validation

• Determine crystal structures and binding sites of
  FAC molecules
• Determine mechanical properties of molecules of
  interest
• AFM
• Optical Tweezers
• Single Molecule Fluorescence

Mehta et al., 1999 Lang et al., 2002
21
Experimentation/Model Validation

• Recreate FAC in vitro (within microfluidic
  chambers) and subject to external loadings
• Extend model to analyze kinetically varying FAC
• Analyze FAC from a finite elements perspective,
  taking into account individual domain linkages,
  deformations, and unfolding

22
Experimentation/Model Validation

• Study effects of mechanical deformations on
  catalytical activities of enzymes and proteins
  present in FAC

Catalysis rate function of deformation kk(?x)
Enzyme
23
Model Analysis

• Loading dependent response
• Static loading
• Dynamic loading
• Complex transient response
• Identification of resonant frequency
• Deformation of proteins dictated by their
  mechanical properties
• Suggests that mechanochemical coupling occurs at
  FAC
• Supports localized signaling

24
Conclusions

• Model needs to be complemented by experimental
  data
• Results provide insight into protein synthesis of
  dynamically loaded cells in culture
• Deformations predicted by model correlate well
  with single molecule simulations and experimental
  data
• Does not rule out energy propagation
  as described by tensegrity and
  percolation models

Shafrir and Forgacs, 2001
25
Acknowledgements

• Ali Khademhosseini
• Doug Lauffenburger
• Paul Matsudaira
• BE.400 Class

26
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