Cell motility as an energy minimization process.

The dynamics of active matter driven by interacting molecular motors has a nonpotential structure at the local scale. However, we show that there exists a quasipotential effectively describing the collective self-organization of the motors propelling a cell at a continuum active gel level. Such a model allows us to understand cell motility as an active phase transition problem between the static and motile steady-state configurations that minimize the quasipotential. In particular, both configurations can coexist in a metastable fashion and a small stochastic disorder in the gel is sufficient to trigger an intermittent cell dynamics where either static or motile phases are more probable, depending on which state is the global minimum of the quasipotential.

Tug-of-war between stretching and bending in living cell sheets.

The balance between stretching and bending deformations characterizes shape transitions of thin elastic sheets. While stretching dominates the mechanical response in tension, bending dominates in compression after an abrupt buckling transition. Recently, experimental results in suspended living epithelial monolayers have shown that, due to the asymmetry in surface stresses generated by molecular motors across the thickness e of the epithelium, the free edges of such tissues spontaneously curl out-of-plane, stretching the sheet in-plane as a result. This suggests that a competition between bending and stretching sets the morphology of the tissue margin. In this paper, we use the framework of non-Euclidean plates to incorporate active pre-strain and spontaneous curvature to the theory of thin elastic shells. We show that, when the spontaneous curvature of the sheet scales like 1/e, stretching and bending energies have the same scaling in the limit of a vanishingly small thickness and therefore both compete, in a way that is continuously altered by an external tension, to define the three-dimensional shape of the tissue.

Active gel segment behaving as an active particle.

We reduce a one-dimensional model of an active segment (AS), which is used, for instance, in the description of contraction-driven cell motility, to a zero-dimensional model of an active particle (AP) characterized by two internal degrees of freedom: position and polarity. Both models give rise to hysteretic force-velocity relations showing that an active agent can support two opposite polarities under the same external force and that it can maintain the same polarity while being dragged by external forces with opposite orientations. This double bistability results in a rich dynamic repertoire which we illustrate by studying static, stalled, motile, and periodically repolarizing regimes displayed by an active agent confined in a viscoelastic environment. We show that the AS and AP models can be calibrated to generate quantitatively similar dynamic responses.

Mechanical stress as a regulator of cell motility.

The motility of a cell can be triggered or inhibited not only by an applied force but also by a mechanically neutral force couple. This type of loading, represented by an applied stress and commonly interpreted as either squeezing or stretching, can originate from extrinsic interaction of a cell with its neighbors. To quantify the effect of applied stresses on cell motility we use an analytically transparent one-dimensional model accounting for active myosin contraction and induced actin turnover. We show that stretching can polarize static cells and initiate cell motility while squeezing can symmetrize and arrest moving cells. We show further that sufficiently strong squeezing can lead to the loss of cell integrity. The overall behavior of the system depends on the two dimensionless parameters characterizing internal driving (chemical activity) and external loading (applied stress). We construct a phase diagram in this parameter space distinguishing between static, motile, and collapsed states. The obtained results are relevant for the mechanical understanding of contact inhibition and the epithelial-to-mesenchymal transition.

Rigidity generation by nonthermal fluctuations.

Active stabilization in systems with zero or negative stiffness is an essential element of a wide variety of biological processes. We study a prototypical example of this phenomenon and show how active rigidity, interpreted as a formation of a pseudowell in the effective energy landscape, can be generated in an overdamped stochastic system. We link the transition from negative to positive rigidity with time correlations in the additive noise, and we show that subtle differences in the out-of-equilibrium driving may compromise the emergence of a pseudowell.

Descending aorta subject-specific one-dimensional model validated against in vivo data.

The aorta plays a major role in the cardiovascular system and its function and structure are primarily affected by aging, eating habits, life style and other cardiovascular risk factors, inducing increased stiffness which is associated with cardiovascular and cerebral morbi-mortality. Our objective was to develop and validate a robust subject-specific one-dimensional wave propagation numerical model of the descending aorta. This model with a cross-sectional area, velocity and pressure formulation is built using geometric and hemodynamic data measured on a specific person and is validated against in vivo data acquired on the same subject at three distinct anatomical locations along the thoracic aorta. We studied seven healthy volunteers, who underwent carotid applanation tonometry and aortic cardiovascular magnetic resonance (CMR). Responses of our model in terms of changes in central pressure waveform with arterial alterations were consistent with previously described physiological knowledge. Quantitative validation averaged over the three descending aortic locations and the seven subjects provided low rms errors (given in percentage of the maximal clinical value) between simulated and CMR data, i.e. area: 10±6%, velocity: 11±3%, flow rate: 9±3%. Finally, we also found low rms (5±2%) when comparing simulated pressure in the proximal aortic location against tonometric carotid pressure curves. In conclusion, this simple model performs similar to more complex models of the entire systemic arterial tree at a fraction of the cost, and could be of major usefulness in the non-invasive and local estimation of proximal biomechanical and hemodynamic indices.

Contraction-driven cell motility.

We propose a mechanism for the initiation of cell motility that is based on myosin-induced contraction and does not require actin polymerization. The translocation of a cell is induced by symmetry breaking of the motor-driven flow, and the ensuing asymmetry gives rise to a steady motion of the center of mass of a cell. The predictions of the model are consistent with observations on keratocytes.