A gradient estimate to a degenerate parabolic equation with a singular absorption term: The global quenching phenomena

We prove global existence of nonnegative solutions to the one dimensional degenerate parabolic problems containing a singular term. We also show the global quenching phenomena for L1 initial datums. Moreover, the free boundary problem is considered in this paper.

Flavonols mediate root phototropism and growth through regulation of proliferation-to-differentiation transition.

Roots normally grow in darkness, but they may be exposed to light. After perceiving light, roots bend to escape from light (root light avoidance) and reduce their growth. How root light avoidance responses are regulated is not well understood. Here, we show that illumination induces the accumulation of flavonols in Arabidopsis thaliana roots. During root illumination, flavonols rapidly accumulate at the side closer to light in the transition zone. This accumulation promotes asymmetrical cell elongation and causes differential growth between the two sides, leading to root bending. Furthermore, roots illuminated for a long period of time accumulate high levels of flavonols. This high flavonol content decreases both auxin signaling and PLETHORA gradient as well as superoxide radical content, resulting in reduction of cell proliferation. In addition, cytokinin and hydrogen peroxide, which promote root differentiation, induce flavonol accumulation in the root transition zone. As an outcome of prolonged light exposure and flavonol accumulation, root growth is reduced and a different root developmental zonation is established. Finally, we observed that these differentiation-related pathways are required for root light avoidance. We propose that flavonols function as positional signals, integrating hormonal and ROS pathways to regulate root growth direction and rate in response to light.