Photoinactivation of photosystem 2 (PS2) results from absorption of so-called "excessive" photon energy. Chlorophyll a fluorescence can be applied to quantitatively estimate the portion of excessive photons by means of the parameter E = (F - F0')/Fm', which reflects the share of the absorbed photon energy that reaches the reaction centers (RCs) of PS2 complexes with QA in the reduced state ('closed' RCs). Data obtained for cotton (Gossypium hirsutum), bean (Phaseolus vulgaris), and arabidopsis (Arabidopsis thaliana) suggest a linear relationship between the total amount of the photon energy absorbed in excess (excessive irradiation) and the decline in PS2 activity, though the slope may differ depending on the species. This relationship was sensitive not only to the leaf temperature but also to treatment with methyl viologen. Such observations imply that the intensity of the oxidative stress as well as the plant's ability to detoxify active oxygen species may interact to determine the damaging potential of the excessive photons absorbed by PS2 antennae. Energy partitioning in PS2 complexes was adjusted during adaptation to irradiation and in response to a decrease in leaf temperature to minimize the excitation energy that is trapped by 'closed' PS2 RCs. The same amount of the excessive photons absorbed by PS2 antennae led to a greater decrease in PS2 activity at warmer temperatures, however, the delay in the development of non-photochemical and photochemical energy quenching under lower temperature resulted in faster accumulation of excessive photons during induction. Irradiance response curves of EF suggest that, at high irradiance (above 700 μmol m-2 s-1), steady-state levels of this parameter tend to be similar regardless of the leaf temperature. and D. Kornyeyev, A. S. Holaday, B. A. Logan.
The concept of the $k$-pairable graphs was introduced by Zhibo Chen (On $k$-pairable graphs, Discrete Mathematics 287 (2004), 11–15) as an extension of hypercubes and graphs with an antipodal isomorphism. In the same paper, Chen also introduced a new graph parameter $p(G)$, called the pair length of a graph $G$, as the maximum $k$ such that $G$ is $k$-pairable and $p(G)=0$ if $G$ is not $k$-pairable for any positive integer $k$. In this paper, we answer the two open questions raised by Chen in the case that the graphs involved are restricted to be trees. That is, we characterize the trees $G$ with $p(G)=1$ and prove that $p(G \square H)=p(G)+p(H)$ when both $G$ and $H$ are trees.