Chiral molecules form a plethora of liquid-crystalline phases, even in equilibrium. Liquid-crystalline phases formed by chiral and active agents have features that are even more counterintuitive. For instance, while in passive matter, chirality tends to cloak itself from the long-wavelength elastic and hydrodynamic properties, activity reveals its effect in cholesteric and chiral columnar phases, leading to unique forms of odd elastic behaviours. Specifically, cholesteric phases display a unique odd elastic force density tangential to the contours of the constant mean curvature of layer undulation. This ultimately leads to the formation of an antiferromagnetically organised, columnar, vortex-lattice array in extensile active cholesteric fluids. Columnar materials which are both polar and chiral surprisingly display two-dimensional odd elasticity, even though the system is three-dimensional. The interplay of this odd elasticity with three-dimensional Stokesian hydrodynamics leads to an oscillatory optical mode.
The interplay of chirality and activity also leads to liquid-crystalline phases without a passive analogue, such as time liquid crystals. In this phase, planar-chiral active elements — spinners — that tend to align with each other trade in rotation symmetry breaking for time-translation symmetry breaking. That is, in these spontaneously rotating aligned states, rotation symmetry is restored in a time-averaged sense. Therefore, while such states are aligned, they escape the celebrated Simha-Ramaswamy instability that plagues uniaxial active suspensions by spinning out of unstable configurations. In my talk, I will discuss both new phases of chiral active liquid crystals and their properties and the effect of activity on classical chiral liquid crystalline phases. I will specifically highlight how the interplay of chirality and activity allows the former to affect dynamic and static properties of ordered states to a much greater degree than in passive soft materials, as summarised above.
Given that most biomaterials are chiral, biological systems ranging in scales from subcellular to all the way to organisms are the natural domain for detecting chiral active liquid crystalline organisations and their effect. Indeed, some of the phases that I will describe in my talk were subsequently observed in in vitro experiments with properties consistent with my predictions. Furthermore, given chiral active liquid crystals have material properties that can, in principle, make them useful for engineering applications, a further important avenue of research will involve synthesising them artificially.

Whether one considers swarming insects, flocking birds, or bacterial colonies, collective motion arises from the coordination of individuals and entails the adjustment of their respective velocities. In particular, in close confinement, such as those encountered by dense cell populations during development or regeneration, collective migration can only arise coordinately. Yet, how individuals unify their velocities is often not understood. Focusing on a finite number of cells in circular confinements, we identify waves of polymerizing actin that function as a pacemaker governing the speed of individual cells. We show that the onset of collective motion coincides with the synchronization of the wave nucleation frequencies across the population. Employing a simpler and more readily accessible mechanical model system of active spheres, we identify the synchronization of the individuals' internal oscillators as one of the essential requirements to reach the corresponding collective state. The mechanical 'toy' experiment illustrates that the global synchronous state is achieved by nearest neighbor coupling. We suggest by analogy that local coupling and the synchronization of actin waves are essential for emergent, self-organized motion of cell collectives.

In this talk, I will describe two biologically inspired systems that can be described using the same geometrical Hamiltonian formalism. The first is ATP synthase proteins which rotate in a biological membrane. The second is swimming micro-organisms such as bacteria or algae confined to a 2D film. I will show that in both cases, the active systems self-assemble into distinct structural states - the rotating proteins rearrange into a hexagonal lattice, whereas the micro-swimmers evolve into sharp lines with a particular tilt. While the two systems differ both on the microscopic, local interaction, as well as the emerging, global structure, I will show that their dynamics originate from similar geometrical conservation laws dictated by a Hamiltonian formalism applicable to a broad class of fluid flows.

Many active biological particles, such as swimming microorganisms or motor-proteins, do work on their environment by going though a periodic sequence of shapes. Interactions between particles can lead to the phase-synchronization of their duty cycles. We consider collective dynamics in a suspension of
such active particles coupled through hydrodynamics. We demonstrate that the emergent non-equilibrium states feature stationary patterned flows and robust unidirectional pumping states under confinement. Moreover the phase-synchronized state of the suspension exhibits spatially robust chimera patterns in which synchronized and phase-isotropic regions coexist within the same system. These findings demonstrate a new route to pattern formation and could guide the design of new active materials. An extension of the same theory for treating ciliated surfaces quantitatively captures the instabilities and flow pupmping behaviour of ciliated carpets and metachronal waves.