Dynamical effects in electron transfer reactions. II. Numerical solution

In part I a reaction–diffusion equation was introduced for the description of electron transfer reactions which are induced by fluctuations in both the solvent polarization and in the intramolecular vibrational coordinates. We analyze the model employing a generalized moment expansion for the time behavior of the survival probability Q(t), i.e., for the fraction of molecules that have not transferred their electron at time t. Numerical and, in the narrow reaction window limit, analytical solutions are given for the average survival times τ. When the contribution of the intramolecular coordinates is appreciable an approximate power‐law behavior τ∝τ^α_L, with 0<α≤1, is found for the dependence of τ on the solvent dielectric relaxation time τ_L, in the large τ_L regime. Within the framework of the generalized moment description Q(t) is approximated as a superposition of several optimized exponential functions. In the small and intermediate τ_L regimes it is found that a single‐ or bi‐exponential description, respectively, is sufficient. Simple formulas for such approximations in terms of the average survival times are given. Furthermore it is demonstrated that in the large τ_L regime a truly multiexponential time behavior for the survival probability is encountered which, over a certain range of time, can appear to be algebraic, i.e., Q(t) ∝t^(−γ). The relation of these results to experimental data is discussed

Low-frequency expansion for probability amplitudes: An alternative approach to certain intramolecular dynamics problems

We present an algorithm to determine the averaged time evolution of the probability amplitude for a nonstationary state in a quantum mechanical system. The algorithm is based on a low‐frequency expansion of the probability amplitude and is related to the generalized moment expansion method which has been applied successfully to the description of dynamic correlation functions in stochastic systems. It is shown that the proposed algorithm gives excellent results for the description of quantum beats in the time evolution of the occupation probability for a nonstationary state in model systems. The relation of the algorithm to other theoretical approaches and the relevance for the description of intramolecular energy transfer processes is discussed

Spinoza

"Spinoza", second edition. Encyclopedia entry for the Springer Encyclopedia of EM Phil and the Sciences, ed. D. Jalobeanu and C. T. Wolfe

Kinetic distance and kinetic maps from molecular dynamics simulation

Characterizing macromolecular kinetics from molecular dynamics (MD) simulations requires a distance metric that can distinguish slowly-interconverting states. Here we build upon diffusion map theory and define a kinetic distance for irreducible Markov processes that quantifies how slowly molecular conformations interconvert. The kinetic distance can be computed given a model that approximates the eigenvalues and eigenvectors (reaction coordinates) of the MD Markov operator. Here we employ the time-lagged independent component analysis (TICA). The TICA components can be scaled to provide a kinetic map in which the Euclidean distance corresponds to the kinetic distance. As a result, the question of how many TICA dimensions should be kept in a dimensionality reduction approach becomes obsolete, and one parameter less needs to be specified in the kinetic model construction. We demonstrate the approach using TICA and Markov state model (MSM) analyses for illustrative models, protein conformation dynamics in bovine pancreatic trypsin inhibitor and protein-inhibitor association in trypsin and benzamidine

Heat Conduction and Entropy Production in a One-Dimensional Hard-Particle Gas

We present large scale simulations for a one-dimensional chain of hard-point particles with alternating masses. We correct several claims in the recent literature based on much smaller simulations. Both for boundary conditions with two heat baths at different temperatures at both ends and from heat current autocorrelations in equilibrium we find heat conductivities kappa to diverge with the number N of particles. These depended very strongly on the mass ratios, and extrapolation to N -> infty resp. t -> infty is difficult due to very large finite-size and finite-time corrections. Nevertheless, our data seem compatible with a universal power law kappa ~ N^alpha with alpha approx 0.33. This suggests a relation to the Kardar-Parisi-Zhang model. We finally show that the hard-point gas with periodic boundary conditions is not chaotic in the usual sense and discuss why the system, when kept out of equilibrium, leads nevertheless to energy dissipation and entropy production.Comment: 4 pages (incl. 5 figures), RevTe

Random Walks on a Fluctuating Lattice: A Renormalization Group Approach Applied in One Dimension

We study the problem of a random walk on a lattice in which bonds connecting nearest neighbor sites open and close randomly in time, a situation often encountered in fluctuating media. We present a simple renormalization group technique to solve for the effective diffusive behavior at long times. For one-dimensional lattices we obtain better quantitative agreement with simulation data than earlier effective medium results. Our technique works in principle in any dimension, although the amount of computation required rises with dimensionality of the lattice.Comment: PostScript file including 2 figures, total 15 pages, 8 other figures obtainable by mail from D.L. Stei

Protein kinase C-dependent signaling controls the midgut epithelial barrier to malaria parasite infection in anopheline mosquitoes.

Anopheline mosquitoes are the primary vectors of parasites in the genus Plasmodium, the causative agents of malaria. Malaria parasites undergo a series of complex transformations upon ingestion by the mosquito host. During this process, the physical barrier of the midgut epithelium, along with innate immune defenses, functionally restrict parasite development. Although these defenses have been studied for some time, the regulatory factors that control them are poorly understood. The protein kinase C (PKC) gene family consists of serine/threonine kinases that serve as central signaling molecules and regulators of a broad spectrum of cellular processes including epithelial barrier function and immunity. Indeed, PKCs are highly conserved, ranging from 7 isoforms in Drosophila to 16 isoforms in mammals, yet none have been identified in mosquitoes. Despite conservation of the PKC gene family and their potential as targets for transmission-blocking strategies for malaria, no direct connections between PKCs, the mosquito immune response or epithelial barrier integrity are known. Here, we identify and characterize six PKC gene family members--PKCδ, PKCε, PKCζ, PKD, PKN, and an indeterminate conventional PKC--in Anopheles gambiae and Anopheles stephensi. Sequence and phylogenetic analyses of the anopheline PKCs support most subfamily assignments. All six PKCs are expressed in the midgut epithelia of A. gambiae and A. stephensi post-blood feeding, indicating availability for signaling in a tissue that is critical for malaria parasite development. Although inhibition of PKC enzymatic activity decreased NF-κB-regulated anti-microbial peptide expression in mosquito cells in vitro, PKC inhibition had no effect on expression of a panel of immune genes in the midgut epithelium in vivo. PKC inhibition did, however, significantly increase midgut barrier integrity and decrease development of P. falciparum oocysts in A. stephensi, suggesting that PKC-dependent signaling is a negative regulator of epithelial barrier function and a potential new target for transmission-blocking strategies

A categorification of Morelli's theorem

We prove a theorem relating torus-equivariant coherent sheaves on toric varieties to polyhedrally-constructible sheaves on a vector space. At the level of K-theory, the theorem recovers Morelli's description of the K-theory of a smooth projective toric variety. Specifically, let $X$ be a proper toric variety of dimension $n$ and let M_\bR = \mathrm{Lie}(T_\bR^\vee)\cong \bR^n be the Lie algebra of the compact dual (real) torus T_\bR^\vee\cong U(1)^n. Then there is a corresponding conical Lagrangian \Lambda \subset T^*M_\bR and an equivalence of triangulated dg categories \Perf_T(X) \cong \Sh_{cc}(M_\bR;\Lambda), where \Perf_T(X) is the triangulated dg category of perfect complexes of torus-equivariant coherent sheaves on $X$ and \Sh_{cc}(M_\bR;\Lambda) is the triangulated dg category of complex of sheaves on M_\bR with compactly supported, constructible cohomology whose singular support lies in $\Lambda$. This equivalence is monoidal---it intertwines the tensor product of coherent sheaves on $X$ with the convolution product of constructible sheaves on M_\bR.Comment: 20 pages. This is a strengthened version of the first half of arXiv:0811.1228v3, with new results; the second half becomes arXiv:0811.1228v

Has overweight become the new normal? Evidence of a generational shift in body weight norms

We test for differences across the two most recent NHANES survey periods (19881994 and 1999 2004) in self-perception of weight status. We find that the probability of self-classifying as overweight is significantly lower on average in the more recent survey, for both men and women, controlling for objective weight status and other factors. Among women, the decline in the tendency to self-classify as overweight is concentrated in the 1735 age range, and, within this range, is more pronounced among women with normal BMI than among those with overweight BMI. Among men, the shift away from feeling overweight is roughly equal across age groups, except that the oldest group (5674) exhibits no difference between surveys. In addition, overweight men exhibit a sharper decline in feeling overweight than normal-weight men. Despite the declines in feeling overweight between surveys, weight misperception did not increase significantly for men and decreased by a sizable margin among women. The shifts in selfclassification are not explained by differences between surveys in body fatness or waist circumference, nor by shifting demographics. We interpret the findings as evidence of a generational shift in social norms related to body weight, and propose various mechanisms to explain such a shift, including: (1) higher average adult BMI and adult obesity rates in the later survey cohort, (2) higher childhood obesity rates in the later survey cohort, and (3) public education campaigns promoting healthy body image. The welfare implications of the observed trends in self-classification are mixed

The social psychology of collective victimhood

Collective victimhood, which results from the experience of being targeted as members of a group, has powerful effects on individuals and groups. The focus of this Special Issue is on how people respond to collective victimhood and how these responses shape intergroup relations. We introduce the Special Issue with an overview of emerging social psychological research on collective victimhood. To date, this research has focused mostly on destructive versus positive consequences of collective victimhood for relations with an adversary group, and examined victim groups' needs, victim beliefs, and underlying social identity and categorization processes. We identify several neglected factors in this literature, some of which are addressed by the empirical contributions in the current issue. The Special Issue offers novel perspectives on collective victimhood, presenting findings based on a diverse range of methods with mostly community samples that have direct and vicarious experiences of collective harm in different countries