The mechanochemistry of cytoskeletal force generation

Abstract

In this communication, we propose a model to study the non-equilibrium process by which actin stress fibers develop force in contractile cells. The emphasis here is on the nonequilibrium thermodynamics, which is necessary to address the mechanics as well as the chemistry of dynamic cell contractility. In this setting we are able to develop a framework that relates (a) the dynamics of force generation within the cell and (b) the cell's response to external stimuli to the chemical processes occurring within the cell, as well as to the mechanics of linkage between the stress fibers, focal adhesions and extra-cellular matrix.

A Computational Study of Stress Fiber-Focal Adhesion Dynamics Governing Cell Contractility

“…The stress fiber and the focal adhesions are mechano-chemical subsystems formed by assembly of representative proteins supplied by the cytosol. To substantiate the discussion of the results provided in this paper, we briefly report the main concepts behind the model we adopted; further details can be found in Appendix and elsewhere (Maraldi and Garikipati, 2014;Olberding et al, 2010). In the model, the stress fiber is considered to span between two focal adhesions and to be always under tension; hence, its reference length, x 0 sf , is fixed, as it would not be possible to add proteins at its ends without first abrogating the tension.…”

“…On the other hand, protein binding/unbinding is allowed to occur anywhere along the focal adhesion; however, to compute the relevant kinematic quantities for this sub-system, only the binding rates at its ends need to be tracked. The force is assumed to be uniformly distributed along the focal adhesion and through the stress fiber's thickness (Maraldi and Garikipati, 2014).…”

“…The number of stress fiber representative proteins and the focal adhesion distal and proximal ends' positions (N sf , x d and x p , respectively) are the variables tracked with respect to time. The ordinary differential equations constituting the model are (Maraldi and Garikipati, 2014;Olberding et al, 2010):…”

“…2 For configurations in region FA-c of the response map, a similar discussion is provided in Appendix. The force within the system, P , is often referred to as the contractile force in literature; however, we prefer not to use this terminology, as, according to the stress fiber constitutive model used for the present study (Maraldi and Garikipati, 2014), this force depends not only on contractility, but also on the passive elastic or viscoelastic response of all the sub-systems (see Eqs. (5) in Appendix, and the discussion on stress fiber rheology in the Model Section) and on loads external to the system (see the discussion related to Fig.…”

“…In this paper, we use a recently developed model for the coupled mechano-chemical response of stress fiber-focal adhesion systems to study the development of contractile force, as well as the behavior of such systems under load. The model is based on non-equilibrium thermodynamics and has been described in detail in a work by Maraldi and Garikipati (Maraldi and Garikipati, 2014). Our focus here is on the modes of generation and decay of the force in the system, as well as on the growth and disassembly of the stress fibers and focal adhesions.…”