Periodic Reporting for period 1 - NewGenActive (A New Generation of Active Matter Models)
Reporting period: 2022-09-01 to 2024-08-31
The collective behavior of biological systems is today an intriguing open challenge in several aspects. Biological systems differ from non-living, passive systems because of the continuous injection and dissipation of energy at the single-cell level. This particular feature enables fascinating emergent behavior with important biological functions. For instance, epithelial tissues are made by densely packed cells whose size oscillations synchronize in time and propagate forming wave patterns, which are able to propagate stress forces more efficiently. These mechanisms are crucial in key biological functions such as dorsal closure in embryogenesis and wound healing. Similarly, cardiac cells contracts and expand at every heartbeat following the propagation of an electric pulse originated in the heart: physiological activity corresponds to a regular wave propagation, whereas the emergence of heterogeneities gives rise to irregular waves leading to tachycardia and ventricular fibrillation. A microscopic, physically-based understanding of such collective behavior represents an outstanding challenge and has potential strong impact in the treatment of such disorders.
NewGenActive propose a new generation of active matter models to elucidate the emergence of the collective behavior above-mentioned. Active matter is a fertile research framework, developed in the last three decades to describe the collective behavior of active motile systems, i.e. collectives whose units can individually sustain a self-propelled motion in absence of external mechanical forces. Typical examples of such systems are bacteria, fishes, birds, or pedestrian. Because of its intrinsic non-equilibrium nature, active behavior is not constrained by equilibrium laws. As a direct consequence, non-equilibrium phases such as flocking (when a group of birds fly in the same direction) or motility-induced phase separation (when repulsive particles cluster together) emerge experimentally and have been theoretically explained.
The physics of dense tissues such as cardiac and epithelial tissues presents different challenges. In these cases, the position of the particles is almost fixed in time, while their shape and size change because of activity. The main objective of NewGenActive is then understanding how active shape changes affect the collective dynamics of dense systems. To do so, we introduce a new generation of active matter models whose active ingredient is the capability to change the cell's size or shape, rather then introducing a self-propulsion as in motile active matter. The project aims at understanding the emergence of collective behavior depending on the microscopic interactions between the cells.
The project therefore pursues the definition of a new class of active models with the following objectives:
1) unveil the minimal ingredients to observe the emergence of size waves in a system of actively deformable particles;
2) exploit the model introduced to understand the effect of anisotropy on the dynamics (i.e. non-circular cells);
3) investigate the effect of an energy potential associated to internal degrees of freedom regulating the sizes and the emergence of liquid-liquid phase separation;
4) formulate a thermodynamically consistent framework to investigate the energy fluxes in deformable active particles.
NewGenActive propose a new generation of active matter models to elucidate the emergence of the collective behavior above-mentioned. Active matter is a fertile research framework, developed in the last three decades to describe the collective behavior of active motile systems, i.e. collectives whose units can individually sustain a self-propelled motion in absence of external mechanical forces. Typical examples of such systems are bacteria, fishes, birds, or pedestrian. Because of its intrinsic non-equilibrium nature, active behavior is not constrained by equilibrium laws. As a direct consequence, non-equilibrium phases such as flocking (when a group of birds fly in the same direction) or motility-induced phase separation (when repulsive particles cluster together) emerge experimentally and have been theoretically explained.
The physics of dense tissues such as cardiac and epithelial tissues presents different challenges. In these cases, the position of the particles is almost fixed in time, while their shape and size change because of activity. The main objective of NewGenActive is then understanding how active shape changes affect the collective dynamics of dense systems. To do so, we introduce a new generation of active matter models whose active ingredient is the capability to change the cell's size or shape, rather then introducing a self-propulsion as in motile active matter. The project aims at understanding the emergence of collective behavior depending on the microscopic interactions between the cells.
The project therefore pursues the definition of a new class of active models with the following objectives:
1) unveil the minimal ingredients to observe the emergence of size waves in a system of actively deformable particles;
2) exploit the model introduced to understand the effect of anisotropy on the dynamics (i.e. non-circular cells);
3) investigate the effect of an energy potential associated to internal degrees of freedom regulating the sizes and the emergence of liquid-liquid phase separation;
4) formulate a thermodynamically consistent framework to investigate the energy fluxes in deformable active particles.
The first task has been the formulation of the lattice model of pulsating particles, mimicking the molecular dynamics of deformable active particles. The size pulsation has been represented as an internal discrete degree of freedom and the position of the particle has been constrained to move on a lattice. This choice allowed to exploit the vast literature over statistical mechanics of lattice dynamics. Also, the definition of the microscopic dynamics allowed to simulate the collective behavior numerically. At the same time, we performed analytical progress by deriving the fluctuating hydrodynamic equations of the system.
The microscopic simulations have confirmed the presence of the four phases observed in molecular dynamics: homogeneous phases (disorder, cycles and arrest) and heterogeneous (wave propagation). Remarkably, the arrested phase appears even in absence of repulsive interactions: instead, the discreteness of lattice dynamics breaks the rotational invariance of the phase dynamics and stabilizes the arrested phase. Summarizing, the competition between cycles and arrest leading to wave propagation is allowed only if some physical mechanism is breaking the phase invariance of the dynamics. This result elucidates the findings from numerical simulations and molecular dynamics. The order of the transition can also be characterized by numerical simulations.
The project unveils how the existence of an arrested state needs an explicit symmetry breaking and how waves emerge from the competition between cycling and arrest at intermediate diffusion rates.
Hydrodynamic equations with noise have been derived in a controlled framework. The size dynamics can be represented by a complex order parameter; the latter follows a modified complex Ginzburg-Landau equation (CGLE) with explicit symmetry breaking in the vicinity of the disordered transition. The properties of the noise have been derived from the microscopic dynamics. The hydrodynamic equation obtained identifies a new class of pulsating field theories where explicit symmetry breaking controls the pattern formation; the limit of large number of internal states – connecting with molecular dynamics - has shown to be not trivial and is currently object of further research.
Furthermore, the project investigated the dynamics of actively deforming particles with an internal energy landscape and actively deformable ellipsoids. In the former case, we observed that a sufficiently complex landscape leads to liquid-liquid phase separation as a long-lived transient observed in molecular dynamics. The hydrodynamic equations have been obtained with a mapping to equilibrium and have shown predictive power in the formulation of a phase diagram when asymmetry is included in the internal energy.
Numerical simulations of actively pulsating ellipsoids have shown the robustness of wave propagation to the cell’s anisotropy. Three different pulsation mechanisms have been introduced, accounting for different choices in the ellipsoidal axis dynamics. Orientational order appears at high density depending on the pulsation mechanism. Finally, the elliptical shape allows a size-conserving pulsation which has numerically shown rich patterns in wave propagation.
The results of the first task are currently under review in Physical Review Letters and have been submitted to the arXiv repository. The manuscripts containing results of the second and third tasks are currently in preparation.
The microscopic simulations have confirmed the presence of the four phases observed in molecular dynamics: homogeneous phases (disorder, cycles and arrest) and heterogeneous (wave propagation). Remarkably, the arrested phase appears even in absence of repulsive interactions: instead, the discreteness of lattice dynamics breaks the rotational invariance of the phase dynamics and stabilizes the arrested phase. Summarizing, the competition between cycles and arrest leading to wave propagation is allowed only if some physical mechanism is breaking the phase invariance of the dynamics. This result elucidates the findings from numerical simulations and molecular dynamics. The order of the transition can also be characterized by numerical simulations.
The project unveils how the existence of an arrested state needs an explicit symmetry breaking and how waves emerge from the competition between cycling and arrest at intermediate diffusion rates.
Hydrodynamic equations with noise have been derived in a controlled framework. The size dynamics can be represented by a complex order parameter; the latter follows a modified complex Ginzburg-Landau equation (CGLE) with explicit symmetry breaking in the vicinity of the disordered transition. The properties of the noise have been derived from the microscopic dynamics. The hydrodynamic equation obtained identifies a new class of pulsating field theories where explicit symmetry breaking controls the pattern formation; the limit of large number of internal states – connecting with molecular dynamics - has shown to be not trivial and is currently object of further research.
Furthermore, the project investigated the dynamics of actively deforming particles with an internal energy landscape and actively deformable ellipsoids. In the former case, we observed that a sufficiently complex landscape leads to liquid-liquid phase separation as a long-lived transient observed in molecular dynamics. The hydrodynamic equations have been obtained with a mapping to equilibrium and have shown predictive power in the formulation of a phase diagram when asymmetry is included in the internal energy.
Numerical simulations of actively pulsating ellipsoids have shown the robustness of wave propagation to the cell’s anisotropy. Three different pulsation mechanisms have been introduced, accounting for different choices in the ellipsoidal axis dynamics. Orientational order appears at high density depending on the pulsation mechanism. Finally, the elliptical shape allows a size-conserving pulsation which has numerically shown rich patterns in wave propagation.
The results of the first task are currently under review in Physical Review Letters and have been submitted to the arXiv repository. The manuscripts containing results of the second and third tasks are currently in preparation.
The project established a systematic framework for the investigation of the many-body dynamics of actively deformable particles. The introduction of size pulsation as a new active feature of single units leads to robust collective behavior with numerical and analytical results. The hydrodynamic equations derived lead to as a new class of hydrodynamic theories whose general behavior is yet to be investigated: their generality may have the required flexibility to interpret many observation in pattern formation and guide the development of pulsating active matter at the boundary between non-equilibrium statistical physics and soft matter.
Finally, the project provides a framework where quantitative comparisons with experiments are now possible. Further research may investigate the adherence of theory and experimental results and modify the microscopic model following information from biological systems.
Finally, the project provides a framework where quantitative comparisons with experiments are now possible. Further research may investigate the adherence of theory and experimental results and modify the microscopic model following information from biological systems.