Geometric models for robust encoding of dynamical information into embryonic patterns

During development, cells gradually assume specialized fates via changes of transcriptional dynamics, sometimes even within the same developmental stage. For anterior-posterior (AP) patterning in metazoans, it has been suggested that the gradual transition from a dynamic genetic regime to a static one is encoded by different transcriptional modules. In that case, the static regime has an essential role in pattern formation in addition to its maintenance function. In this work, we introduce a geometric approach to study such transition. We exhibit two types of genetic regime transitions arising through local or global bifurcations, respectively. We find that the global bifurcation type is more generic, more robust, and better preserves dynamical information. This could parsimoniously explain common features of metazoan segmentation, such as changes of periods leading to waves of gene expressions, ‘speed/frequency-gradient’ dynamics, and changes of wave patterns. Geometric approaches appear as possible alternatives to gene regulatory networks to understand development.

Time-varying optical vortices enabled by time-modulated metasurfaces

In this paper, generation of optical vortices with time-varying orbital angular momentum (OAM) and topological charge is theoretically demonstrated based on time-modulated metasurfaces with a linearly azimuthal frequency gradient. The topological charge of such dynamic structured light beams is shown to continuously and periodically change with time evolution while possessing a linear dependence on time and azimuthal frequency offset. The temporal variation of OAM yields a self-torqued beam exhibiting a continuous angular acceleration of light. The phenomenon is attributed to the azimuthal phase gradient in space-time generated by virtue of the spatiotemporal coherent path in the interference between different frequencies. In order to numerically authenticate this newly introduced concept, a reflective dielectric metasurface is modelled consisting of silicon nanodisk heterostructures integrated with indium-tin-oxide and gate dielectric layers on top of a mirror-backed silicon slab which renders an electrically tunable guided mode resonance mirror in near-infrared regime. The metasurface is divided into several azimuthal sections wherein nanodisk heterostructures are interconnected via nanobars serving as biasing lines. Addressing azimuthal sections with radio-frequency biasing signals of different frequencies, the direct dynamic photonic transitions of leaky-guided modes are leveraged for realization of an azimuthal frequency gradient in the optical field. Generation of dynamic twisted light beams with time-varying OAM by the metasurface is verified via performing several numerical simulations. Moreover, the role of modulation waveform and frequency gradient on the temporal evolution and diversity of generated optical vortices is investigated which offer a robust electrical control over the number of dynamic beams and their degree of self-torque. Our results point toward a new class of structured light for time-division multiple access in optical and quantum communication systems as well as unprecedented optomechanical manipulation of objects.

Geometric models for robust encoding of dynamical information into embryonic patterns

During development, cells gradually assume specialized fates via changes of transcriptional dynamics, sometimes even within the same developmental stage. For anterior-posterior (AP) patterning in metazoans, it has been suggested that the gradual transition from a dynamic genetic regime to a static one is encoded by different transcriptional modules. In that case, the static regime has an essential role in pattern formation in addition to its maintenance function. In this work, we introduce a geometric approach to study such transition. We exhibit two types of genetic regime transitions, respectively arising through local or global bifurcations. We find that the global bifurcation type is more generic, more robust, and better preserves dynamical information. This could parsimoniously explain common features of metazoan segmentation, such as changes of periods leading to waves of gene expressions, “speed/frequency-gradient” dynamics, and changes of wave patterns. Geometric approaches appear as possible alternatives to gene regulatory networks to understand development.

Spatiotemporal light control with frequency-gradient metasurfaces

The capability of on-chip wavefront modulation has the potential to revolutionize many optical device technologies. However, the realization of power-efficient phase-gradient metasurfaces that offer full-phase modulation (0 to 2π) and high operation speeds remains elusive. We present an approach to continuously steer light that is based on creating a virtual frequency-gradient metasurface by combining a passive metasurface with an advanced frequency-comb source. Spatiotemporal redirection of light naturally occurs as optical phase-fronts reorient at a speed controlled by the frequency gradient across the virtual metasurface. An experimental realization of laser beam steering with a continuously changing steering angle is demonstrated with a single metasurface over an angle of 25° in just 8 picoseconds. This work can support integrated-on-chip solutions for spatiotemporal optical control, directly affecting emerging applications such as solid-state light detection and ranging (LIDAR), three-dimensional imaging, and augmented or virtual systems.

In-silico study of the ionic current gradients determining left-to-right atrial frequencies during paroxysmal atrial fibrillation

Atrial fibrillation is the most prevalent cardiac arrhythmia. Paroxysmal atrial fibrillation (pAF) may occur in episodes lasting from minutes to days. Recent studies suggest that some pAF episodes present a left-to-right dominant frequency gradient caused by ionic current gradients. However, how each ionic current gradient affects the left-to-right dominant frequency gradient during pAF has not been studied. In this work, we use a 3D model of human atria to study how the ionic current gradients affect the dominant frequency gradient during pAF induced by continuous ectopic activity. The role of the specific gradients of acetylcholine-activated potassium current ( IKACh) and inward-rectifier potassium current ( IK1) on determining the left-to-right dominant frequency gradient was assessed. The main outcome of this study is that either or both of the IKACh or IK1 gradients are necessary to induce a left-to-right dominant frequency gradient during pAF. However, both gradients are necessary to the left atrium maintaining, by itself, the pAF episode. These findings have potentially important implications for the development of atrial-selective therapeutic approaches.