Modeling Confined Cell Migration Mediated by Cytoskeleton Dynamics
Abstract
:1. Introduction
2. Materials and Methods
2.1. Mathematical Model
2.1.1. Mechanical Equilibrium
2.1.2. Constitutive Law
2.1.3. Reaction–Diffusion Equations
2.1.4. External Forces
2.1.5. Cell Domain Growth
2.1.6. Adhesion Process
2.2. Numerical Method
- Firstly, we use the stable Crank–Nicholson scheme to compute the displacement u, and consequently the stress tensor at each time step through the corresponding constitutive law.
- Secondly, we update the actin and myosin concentrations (bound and free) using a similar scheme.
- If an external stress is applied, the cell is deformed mechanically. If the growth stress threshold is reached, the membrane is detached from the actin creating new space and Equations (16) and (17) are solved.
- Finally, after updating the variables, we check if the compression stress threshold is reached in order to update the friction coefficient with the substrate .
3. Results
3.1. Influence of Actin and Myosin Densities on Cell Mechanics
3.2. Sensitivity Analysis
- the initial cell length , increasing its value to 20 µm,
- the characteristic myosin stress , decreasing its value to 0.1 pN/µm2, in order to study the influence of the cell contractility in its movement,
- the time interval of application of the surface load, deactivating the load at = 2.5 s.
4. Discussion and Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Parameter | Symbol | Value | Source |
---|---|---|---|
Substrate friction | 103 pNs/µm3 | [4] | |
Reduced substrate friction | 10−3 pNs/µm3 | Estimated | |
Initial Young modulus | 104 pNs/µm2 | [4] | |
Myosin stress | 103 pNs/µm2 | [4] | |
Bound actin and myosin diffusion coefficient | 0.1 µm2/s | [4] | |
Free actin and myosin diffusion coefficient | 104 µm2/s | Estimated | |
Activation rate for bound actin | 0.067 s−1 | [22] | |
Inactivation rate for bound actin | 0.9 s−1 | [22] | |
Bound actin maximal rate | 1 s−1 | [22] | |
Bound actin saturation parameter | K | 1 µM | [22] |
Activation rate for bound myosin | 0.25 s−1 | Estimated | |
Depolymerization rate for bound myosin | 0.02 s−1 | Estimated |
Parameter | Symbol | Value |
---|---|---|
Initial length of the cell body | 10 µm | |
Simulation spatial step | 0.1 µm | |
Total time of the simulation | T | 10 s |
Simulation time step | 0.01 s | |
Stress threshold for growth | 500 pN | |
Stress threshold for contraction | 750 pN | |
Activation time | 2 s | |
Activation stress | 25,000 pN | |
Deactivation time | 2.1 s | |
Deactivation stress | 500 pN |
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Sánchez, M.T.; García-Aznar, J.M. Modeling Confined Cell Migration Mediated by Cytoskeleton Dynamics. Computation 2018, 6, 33. https://doi.org/10.3390/computation6020033
Sánchez MT, García-Aznar JM. Modeling Confined Cell Migration Mediated by Cytoskeleton Dynamics. Computation. 2018; 6(2):33. https://doi.org/10.3390/computation6020033
Chicago/Turabian StyleSánchez, María Teresa, and José Manuel García-Aznar. 2018. "Modeling Confined Cell Migration Mediated by Cytoskeleton Dynamics" Computation 6, no. 2: 33. https://doi.org/10.3390/computation6020033