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

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

Nanosecond laser photolysis studies of chlorosomes and artificial aggregates containing bacteriochlorophyll e: Evidence for the proximity of carotenoids and bacteriochlorophyll a in chlorosomes from Chlorobium phaeobacteroides strain CL1401

Time-resolved, laser-induced changes in absorbance, ΔA(λ; t), have been recorded with a view to probing pigment–pigment interactions in chlorosomes (control as well as carotenoid-depleted) and artificial aggregates of bacteriochlorophyll e (BChle). Control chlorosomes were isolated from Chlorobium phaeobacteroides strain CL1401, whose chromophores comprise BChle, bacteriochlorophyll a (BChla) and several carotenoid (Car) pigments; Car-depleted chlorosomes, from cells grown in cultures containing 2-hydroxybiphenyl. Artificial aggregates were prepared by dispersing BChle in aqueous phase in the presence of monogalactosyl diglyceride. In chlorosomes ΔA(λ; t) shows, besides a signal attributable to triplet Car (with a half-life of about 4 μs), signals in the Qy regions of both BChl. The BChla signal decays at the same rate as the Car signal, which is explained by postulating that some Car are in intimate contact with some baseplate BChla pigments, and that when a ground-state Car changes into a triplet Car, the absorption spectrum of its BChla neighbors undergoes a concomitant change (termed transient environment-induced perturbation). The signal in the Qy-region of BChle behaves differently: its amplitude falls, under reducing conditions, by more than a factor of two during the first 0.5 μs (a period during which the Car signal suffers negligible diminution), and is much smaller under nonreducing conditions. The BChle signal is also attributed to transient environment-induced perturbation, but in this case the perturber is a BChle photoproduct (probably a triplet or a radical ion). The absence of long-lived BChle triplets in all three systems, and of long-lived BChla triplets in chlorosomes, indicates that BChle in densely packed assemblies is less vulnerable to photodamage than monomeric BChle and that, in chlorosome, BChla rather than BChle needs, and receives, photoprotection from an adjacent Car.Research Council of Norway. EU (contract FMRX-CT96-0081)Peer reviewe

Analytic results for Gaussian wave packets in four model systems: II. Autocorrelation functions

The autocorrelation function, A(t), measures the overlap (in Hilbert space) of a time-dependent quantum mechanical wave function, psi(x,t), with its initial value, psi(x,0). It finds extensive use in the theoretical analysis and experimental measurement of such phenomena as quantum wave packet revivals. We evaluate explicit expressions for the autocorrelation function for time-dependent Gaussian solutions of the Schrodinger equation corresponding to the cases of a free particle, a particle undergoing uniform acceleration, a particle in a harmonic oscillator potential, and a system corresponding to an unstable equilibrium (the so-called `inverted' oscillator.) We emphasize the importance of momentum-space methods where such calculations are often more straightforwardly realized, as well as stressing their role in providing complementary information to results obtained using position-space wavefunctions.Comment: 18 pages, RevTeX, to appear in Found. Phys. Lett, Vol. 17, Dec. 200