Cellular and Molecular Bioengineering

, Volume 6, Issue 4, pp 449–459

Master Equation-Based Analysis of a Motor-Clutch Model for Cell Traction Force


DOI: 10.1007/s12195-013-0296-5

Cite this article as:
Bangasser, B.L. & Odde, D.J. Cel. Mol. Bioeng. (2013) 6: 449. doi:10.1007/s12195-013-0296-5


Microenvironmental mechanics play an important role in determining the morphology, traction, migration, proliferation, and differentiation of cells. A stochastic motor-clutch model has been proposed to describe this stiffness sensitivity. In this work, we present a master equation-based ordinary differential equation (ODE) description of the motor-clutch model, from which we derive an analytical expression to for a cell’s optimum stiffness (i.e., the stiffness at which the traction force is maximal). This analytical expression provides insight into the requirements for stiffness sensing by establishing fundamental relationships between the key controlling cell-specific parameters. We find that the fundamental controlling parameters are the numbers of motors and clutches (constrained to be nearly equal), and the time scale of the on–off kinetics of the clutches (constrained to favor clutch binding over clutch unbinding). Both the ODE solution and the analytical expression show good agreement with Monte Carlo motor-clutch output, and reduce computation time by several orders of magnitude, which potentially enables long time scale behaviors (hours–days) to be studied computationally in an efficient manner. The ODE solution and the analytical expression may be incorporated into larger scale models of cellular behavior to bridge the gap from molecular time scales to cellular and tissue time scales.


Adhesion Mechanosensing Master equation Durotaxis F-actin Myosin Cytoskeletal dynamics Multi-scale modeling Monte Carlo simulation 

Supplementary material

12195_2013_296_MOESM1_ESM.docx (37 kb)
Supplementary material 1 (DOCX 38 kb)
12195_2013_296_MOESM2_ESM.pptx (51 kb)
Supplementary material 2 (PPTX 52 kb)
12195_2013_296_MOESM3_ESM.pptx (124 kb)
Supplementary material 3 (PPTX 125 kb)
12195_2013_296_MOESM4_ESM.pptx (452 kb)
Supplementary material 4 (PPTX 452 kb)

Copyright information

© Biomedical Engineering Society 2013

Authors and Affiliations

  1. 1.Department of Biomedical EngineeringUniversity of MinnesotaMinneapolisUSA

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