Hydrodynamic synchronization is a fundamental physical phenomenon by which self-sustained oscillators communicate through perturbations in the surrounding fluid and converge to a stable synchronized state. This is an important factor for the emergence of regular and coordinated patterns in the motions of cilia and flagella. When dealing with biological systems, however, it is always hard to disentangle internal signaling mechanisms from external purely physical couplings. We have used the combination of two-photon polymerization and holographic optical trapping to build a mesoscale model composed of chiral propellers rotated by radiation pressure. The two microrotors can be synchronized by hydrodynamic interactions alone although the relative torques have to be finely tuned. Dealing with a micron sized system we treat synchronization as a stochastic phenomenon and show that the phase lag between the two microrotors is distributed according to a stationary Fokker-Planck equation for an overdamped particle over a tilted periodic potential. Synchronized states correspond to minima in this potential whose locations are shown to depend critically on the detailed geometry of the propellers. Synchronization is at the basis of a wide variety of fascinating and important phenomena in physics, biology, and engineering. From coupled Josephson junctions [1] to cardiac pacemaker cells [2], the presence of a weak interaction between two or more self-sustained oscillators often leads to the emergence of synchronous patterns [3]. At the micron scale of cells and bacteria, hydrodynamic interactions provide a strong and long-ranged mechanism for coupling [4]. Since synchronization phenomena are known to occur even in the presence of extremely weak and subtle couplings, it is quite natural to expect strong synchronous behavior in such a strongly coupled regime. The presence of a strong coupling, however, is not a sufficient condition for synchronization [5,6], and the role of hydrodynamic interactions for the emergence of synchronous behaviors in flagella [7][8][9] and cilia [10-13] is still the subject of a lively debate [14]. In the case of waving sheets [5], kinematic reversibility can destroy synchronization when the sheets have reflection symmetry. For the same reason, a collection of rigid rotors, spinning around fixed axes and coupled through hydrodynamic interactions, will appear as the same physical system evolving on a time reversed trajectory when we change sign to all applied torques. Such reversible dynamics cannot give rise to any synchronization behavior that is, by definition, an irreversible process. This symmetry upon torque reversal can be broken by using phase dependent torques [6] or, alternatively, by introducing some degree of mechanical flexibility in the form of internal degrees of freedom with finite stiffness [15,16]. In the latter case, when we reverse the sign of applied torques, internal forces will not change their sign and the system will not trace back its history. As a consequence, synchronization...
We introduce a system of light driven microscopic autonomous moving particles that move on a flat surface. The design is simple, yet effective: Micrometer sized objects with wedge shape are produced by photopolymerization, they are covered with a reflective surface. When the area of motion is illuminated perpendicularly from above, the light is deflected to the side by the wedge shaped objects, in the direction determined by the position and orientation of the particles. The momentum change during reflection provides the driving force for an effectively autonomous motion. The system is an efficient tool to study self propelled microscopic robots.
Fluorescent observation of cells generally suffers from the limited axial resolution due to the elongated point spread function of the microscope optics. Consequently, three-dimensional imaging results in axial resolution being several times worse than the transversal. The optical solutions to this problem usually require complicated optics and extreme spatial stability. A straightforward way to eliminate anisotropic resolution is to fuse images recorded from multiple viewing directions achieved mostly by the mechanical rotation of the entire sample. In the presented approach, multiview imaging of single cells is implemented by rotating them around an axis perpendicular to the optical axis by means of holographic optical tweezers. For this, the cells are indirectly trapped and manipulated with special microtools made with two-photon polymerization. The cell is firmly attached to the microtool and is precisely manipulated with 6 degrees of freedom. The total control over the cells position allows for its multiview fluorescence imaging from arbitrarily selected directions. The image stacks obtained this way are combined into one 3D image array with a special image processing algorithm resulting in isotropic optical resolution. The presented tool and manipulation scheme can be readily applied in various microscope platforms.
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