We have developed a thermodynamically consistent model for a simplified configuration which has been studied experimentally: the self-assembly of actin networks on biomimetic beads. In this system the bead surface initiates the growth of actin molecules suspended in solution into a network. Due to the curved geometry, the network growth leads to the build-up of residual stresses in the network.
Using the framework of linear non-equilibrium thermodynamics, we have derived the equations of mechanical equilibrium of the pre-stressed network and the equations of motion of the network boundaries. We could show, that (i) the coupling between mechanical pre-stresses and network growth results in symmetry-properties which are a direct consequence of the employed gradient dynamics and (ii) that the pre-stresses trigger a symmetry-breaking in the network growth. This indicates that cell polarization might be a natural consequence of mechanical pre-stresses in addition to complex cellular signalling cascades.