A Note on the Kinetics of Diffusion-mediated Reactions

The prevalent scheme of a diffusion-mediated bimolecular reaction $A+B\rightarrow P$ is an adaptation of that proposed by Briggs and Haldane for enzyme action [{\em Biochem J.\/}, 19:338--339, 1925]. The purpose of this Note is to explain, {\em by using an argument involving no mathematics\/}, why the breakup of the encounter complex cannot be described, except in special circumstances, in terms of a first-order process $\{AB\}\rightarrow A+B$. Briefly, such a description neglects the occurrence of re-encounters, which lie at the heart of Noyes's theory of diffusion-mediated reactions. The relation k=\alpha k_{\mbox{\scriptsize e}} becomes valid only when $\alpha$ (the reaction probability per encounter) is very much smaller than unity (activation-controlled reactions), or when $\beta$ (the re-encounter probability) is negligible (as happens in a gas-phase reaction). References to some works (by the author and his collaborators) which propound the correct approach for finding $k$ are also supplied.Comment: 4 pages, 1 figur

Portfolio optimisation with higher moments of risk at the Pakistan Stock Exchange

Stock markets play an important role in spurring economic growth and development through diversification opportunities. However, diversification cannot be truly achieved if we continue to ignore additional dimensions of risk, namely skewness and kurtosis. This study incorporates higher moments of risk to form a mean-varianceskewness-kurtosis based framework for portfolio optimisation. Inclusion of higher moments in optimisation framework acknowledges the risk of asymmetric returns and fat-tail risk and can help investors in formulating optimal portfolios of stocks which can be significantly divergent from the ones they obtain through the Markowitz meanvariance optimisation. Our results confirm the presence of tradeoff between returns and additional dimensions of risk in Pakistan Stock Exchange (PSX) and strongly suggest including them in the optimisation framework to avoid sub-optimal decisions and to curtail exposure towards higher moments of risks

Endogenous Singlet Oxygen Photosensitizers in Plants.

Singlet oxygen, a highly reactive oxygen species, is inherently produced in chloroplasts of plants. Chlorophylls are used by plants to harvest light and to transport the singlet electronic excitation from the antenna complexes to the reaction centre (RC) of photosystem I (PSI) and PSII. However, chlorophylls are also efficient photosensitizers of singlet oxygen when they are isolated, when the excitation energy flow is impaired in the antenna complexes, or when the electron transport in PSII is inhibited. In the last case, chlorophyll triplets are formed, and transfer their electronic excitation to molecular oxygen. That chlorophylls act as donors of singlet excitation to other chlorophylls or as donors of triplet excitation to carotenoids as well as molecular oxygen makes singlet oxygen a constant threat for plants. However, plants have developed protection mechanisms for dealing with the danger. Several molecular processes work together in chloroplasts to cope with photosensitization of singlet oxygen and to minimize the resulting damage. Protection utilizes two strategies: to forestall the formation of singlet oxygen (either by preventing the formation of the would-be sensitizer or through deactivating it by a quencher other than molecular oxygen), and to quench, by physical or chemical means, any singlet oxygen that does get formed. Among the photosynthetic complexes, PSII is unique in that its primary electron donor is unprotected by carotenoids and singlet oxygen oxidizes the pigments of PSII RC; intriguingly the carotenoid oxidation products are signalling molecules that can reprogram gene expression. Finally, the distance over which singlet oxygen can diffuse in a viscous cellular medium, as found inside chloroplasts, is analysed.K.R.N and J.B.A are very grateful to the Research Council of Norway (Project 191102) and Junta de Castilla y León (Project CSI002A10-2).Peer reviewe