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Research Papers

# An Analysis of the Cooperative Mechano-Sensitive Feedback Between Intracellular Signaling, Focal Adhesion Development, and Stress Fiber Contractility

[+] Author and Article Information
Amit Pathak

Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106

Robert M. McMeeking

Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106; Department of Materials, University of California, Santa Barbara, CA 93106; INM Leibniz Institute for New Materials, 66123, Saarbruecken, Germany

Anthony G. Evans

Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106; Department of Materials, University of California, Santa Barbara, CA 93106

Vikram S. Deshpande

Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106; Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK

J. Appl. Mech 78(4), 041001 (Apr 12, 2011) (12 pages) doi:10.1115/1.4003705 History: Received May 07, 2010; Revised October 07, 2010; Posted February 23, 2011; Published April 12, 2011; Online April 12, 2011

## Abstract

Cells communicate with their external environment via focal adhesions and generate activation signals that in turn trigger the activity of the intracellular contractile machinery. These signals can be triggered by mechanical loading that gives rise to a cooperative feedback loop among signaling, focal adhesion formation, and cytoskeletal contractility, which in turn equilibrates with the applied mechanical loads. We devise a signaling model that couples stress fiber contractility and mechano-sensitive focal adhesion models to complete this above mentioned feedback loop. The signaling model is based on a biochemical pathway where $IP3$ molecules are generated when focal adhesions grow. These $IP3$ molecules diffuse through the cytosol leading to the opening of ion channels that disgorge $Ca2+$ from the endoplasmic reticulum leading to the activation of the actin/myosin contractile machinery. A simple numerical example is presented where a one-dimensional cell adhered to a rigid substrate is pulled at one end, and the evolution of the stress fiber activation signal, stress fiber concentrations, and focal adhesion distributions are investigated. We demonstrate that while it is sufficient to approximate the activation signal as spatially uniform due to the rapid diffusion of the $IP3$ through the cytosol, the level of the activation signal is sensitive to the rate of application of the mechanical loads. This suggests that ad hoc signaling models may not be able to capture the mechanical response of cells to a wide range of mechanical loading events.

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## Figures

Figure 7

(a) Comparison of temporal evolution of the signals Ĉ and C¯ in a cell (reference properties) subjected umax=100 nm at a displacement rate u̇app=0.1 nm s−1. The corresponding spatio-temporal evolution of the (a) stress fiber concentration η and (b) focal adhesions as parametrized by ξH/ξo in the cell with infinitely rapid IP3 diffusion (i.e., cell subjected to the signal Ĉ). The spatial distributions are plotted in terms of the undeformed cell coordinate X at five selected times t after the initiation of the mechanical perturbation.

Figure 8

(a) The temporal evolution of Ĉ in a cell subjected umax=100 nm at a displacement rate u̇app=0.1 nm s−1 for three selected values of the IP3 production constant α. All other values of the cell properties are fixed at their reference values. The corresponding steady-state (t=17 h) distributions of (b) stress fiber concentration η and (c) focal adhesions as parametrized by ξH/ξo. The spatial distributions are plotted in terms of the undeformed cell coordinate X.

Figure 9

(a) The temporal evolution of Ĉ in a cell (reference properties) subjected umax=100 nm at three selected values of the applied displacement rate u̇app. The corresponding steady-state (t=17 h) distributions of (b) stress fiber concentration η and (c) focal adhesions as parametrized by ξH/ξo. The spatial distributions are plotted in terms of the undeformed cell coordinate X.

Figure 10

The temporal evolution of Ĉ in a cell (reference properties) subjected to a displacement rate u̇app=0.1 nm s−1 for three selected values of the maximum displacement umax

Figure 1

A sequence of images showing the progression of a Ca2+ wave initiated by the mechanical perturbation of a cardiac myocyte by an AFM tip. The location of the AFM tip is indicated by the arrow. Adapted from Ref. 13.

Figure 5

The spatio-temporal evolution of the stress fiber activation signal C in the cell (reference properties) subjected umax=100 nm at a displacement rate u̇app=0.1 nm s−1. The spatial distributions are plotted in terms of the undeformed cell coordinate X at five selected times t after the initiation of the mechanical perturbation.

Figure 6

The spatio-temporal distribution of the (a) stress fiber concentration η and (b) focal adhesions as parametrized by ξH/ξo in the cell (reference properties) subjected umax=100 nm at a displacement rate u̇app=0.1 nm s−1. The spatial distributions are plotted in terms of the undeformed cell coordinate X at five selected times t after the initiation of the mechanical perturbation. (c) The corresponding spatial distributions of C, η, ξH/ξo, and the low affinity integrins ξL/ξo at approximately steady-state (t=17 h).

Figure 2

Schematic illustrating the cooperative feedback loop between signaling, focal adhesion formation, and stress fiber contractility initiated by an external mechanical perturbation

Figure 3

A sketch illustrating the key biochemical processes involved in the signaling pathways induced by focal adhesion formation and resulting in the activation of the stress fiber contractile machinery

Figure 4

(a) Sketch of the one-dimensional cell adhered to a rigid substrate. A prescribed displacement versus time history is imposed on one end of the cell. (b) The time history of the displacement uapp imposed on the cell in (a). The sketch defines the key loading parameters: the maximum applied umax and the time to at which this displacement is reached.

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