Stress fibers are bundles of actin filaments made contractile by interaction with myosin
minifilaments, and elastic by crosslinking with alpha-actinin and other proteins. The spatial
profile of the polarity of the actin filaments inside contractile actomyosin bundles
is known to be either monotonic (graded) or periodic (alternating) . In the framework
of linear irreversible thermodynamics, we write the constitutive equations for
a one-dimensional, polar, active elastomer and show that the transition from graded to
alternating polarity patterns is a nonequilibrium Lifshitz point, where a diffusion constant
changes sign. Active contractility is a necessary condition for the emergence of
sarcomeric, alternating polarity patterns.
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