We analyze travelling wave (TW) solutions for nonlinear systems consisting of an ODE coupled to a degenerate PDE with a diffusion coefficient that vanishes as the solution tends to zero and blows up as it approaches its maximum value. Stable TW solutions for such systems have previously been observed numerically as well as in biological experiments on the growth of cellulolytic biofilms. In this work, we provide an analytical justification for these observations and prove existence and stability results for TW solutions of such models. Using the TW ansatz and a first integral, the system is reduced to an autonomous dynamical system with two unknowns. Analysing the system in the corresponding phase-plane, the existence of a unique TW is shown, which possesses a sharp front and a diffusive tail, and is moving with a constant speed. The linear stability of the TW in two space dimensions is proven under suitable assumptions on the initial data. Finally, numerical simulations are presented that affirm the theoretical predictions on the existence, stability, and parametric dependence of the travelling waves.
The question of how changes in chemoattractant concentration translate into the chemotactic response of immune cells serves as a paradigm for the quantitative understanding of how cells perceive and process temporal and spatial information. Here, using a microfluidic approach, we analyzed the migration of neutrophil-like HL-60 cells to a traveling wave of the chemoattractants fMLP and leukotriene B4 (LTB4). We found that under a pulsatile wave that travels at a speed of 95 and 170 µm/min, cells move forward in the front of the wave but slow down and randomly orient at the back due to temporal decrease in the attractant concentration.
Red Sea elasmobranch populations are facing alarming declines. Effective conservation efforts require management strategies informed by extensive datasets and by developing an understanding of distribution patterns within the basin, which is currently lacking. This study introduces CERSE (Central and Eastern Red Sea Elasmobranchs), a comprehensive compilation of elasmobranch observations in the central and eastern Red Sea basin following the route of the Red Sea Decade Expedition.
Department of Neurobiology, Harvard Medical School, 220 Longwood Avenue, Boston, MA 02115, USA; Howard Hughes Medical Institute, Harvard Medical School, 220 Longwood Avenue, Boston, MA 02115, USA. Electronic address:
Vibrations are ubiquitous in nature, shaping behavior across the animal kingdom. For mammals, mechanical vibrations acting on the body are detected by mechanoreceptors of the skin and deep tissues and processed by the somatosensory system, while sound waves traveling through air are captured by the cochlea and encoded in the auditory system. Here, we report that mechanical vibrations detected by the body's Pacinian corpuscle neurons, which are distinguished by their ability to entrain to high-frequency (40-1,000 Hz) environmental vibrations, are prominently encoded by neurons in the lateral cortex of the inferior colliculus (LCIC) of the midbrain.
The goal of this article is to identify and understand the fundamental role of spatial symmetries in the emergence of undulatory swimming using an anguilliform robot. Here, the local torque at the joints of the robot is controlled by a chain of oscillators forming a central pattern generator (CPG). By implementing a symmetric CPG with respect to the transverse plane, motor activation waves are inhibited, preventing the emergence of undulatory swimming and resulting in an oscillatory gait.
We explore a biomimetic model that simulates a cell, with the internal cytoplasm represented by a two-dimensional circular domain and the external cortex by a surrounding ring, both modeled using FitzHugh-Nagumo systems. The external ring is dynamically influenced by a pacemaker-driven wave originating from the internal domain, leading to the emergence of three distinct dynamical states based on the varying strengths of coupling. The range of dynamics observed includes phase patterning, the propagation of phase waves, and interactions between traveling and phase waves.
