3-dimensional Gravity from the Turaev-Viro Invariant

We study the $q$-deformed su(2) spin network as a 3-dimensional quantum gravity model. We show that in the semiclassical continuum limit the Turaev-Viro invariant obtained recently defines naturally regularized path-integral $\grave{\rm a}$ la Ponzano-Regge, In which a contribution from the cosmological term is effectively included. The regularization dependent cosmological constant is found to be ${4\pi^2\over k^2} +O(k^{-4})$, where $q^{2k}=1$. We also discuss the relation to the Euclidean Chern-Simons-Witten gravity in 3-dimension.Comment: 11page

Quantum probe and design for a chemical compass with magnetic nanostructures

Magnetic fields as weak as Earth's may affect the outcome of certain photochemical reactions that go through a radical pair intermediate. When the reaction environment is anisotropic, this phenomenon can form the basis of a chemical compass and has been proposed as a mechanism for animal magnetoreception. Here, we demonstrate how to optimize the design of a chemical compass with a much better directional sensitivity simply by a gradient field, e.g. from a magnetic nanostructure. We propose an experimental test of these predictions, and suggest design principles for a hybrid metallic-organic chemical compass. In addition to the practical interest in designing a biomimetic weak magnetic field sensor, our result shows that gradient fields can server as powerful tools to probe spin correlations in radical pair reactions.Comment: 8 pages, 6 figures, comments are welcom

Quantum Zeno Effect Explains Magnetic-Sensitive Radical-Ion-Pair Reactions

Chemical reactions involving radical-ion pairs are ubiquitous in biology, since not only are they at the basis of the photosynthetic reaction chain, but are also assumed to underlie the biochemical magnetic compass used by avian species for navigation. Recent experiments with magnetic-sensitive radical-ion pair reactions provided strong evidence for the radical-ion-pair magnetoreception mechanism, verifying the expected magnetic sensitivities and chemical product yield changes. It is here shown that the theoretical description of radical-ion-pair reactions used since the 70's cannot explain the observed data, because it is based on phenomenological equations masking quantum coherence effects. The fundamental density matrix equation derived here from basic quantum measurement theory considerations naturally incorporates the quantum Zeno effect and readily explains recent experimental observations on low- and high-magnetic-field radical-ion-pair reactions.Comment: 10 pages, 5 figure

Reaction Pathways Based on the Gradient of the Mean First-Passage Time

Finding representative reaction pathways is necessary for understanding mechanisms of molecular processes, but is considered to be extremely challenging. We propose a new method to construct reaction paths based on mean first-passage times. This approach incorporates information of all possible reaction events as well as the effect of temperature. The method is applied to exemplary reactions in a continuous and in a discrete setting. The suggested approach holds great promise for large reaction networks that are completely characterized by the method through a pathway graph.Comment: v2; 4 pages including 5 figure

Polymer Release out of a Spherical Vesicle through a Pore

Translocation of a polymer out of curved surface or membrane is studied via mean first passage time approach. Membrane curvature gives rise to a constraint on polymer conformation, which effectively drives the polymer to the outside of membrane where the available volume of polymer conformational fluctuation is larger. Considering a polymer release out of spherical vesicle, polymer translocation time $\tau$ is changed to the scaling behavior $\tau\sim L^2$ for $R<R_G$, from $\tau\sim L^3$ for $R\gg R_G$, where $L$ is the polymer contour length and $R$, $R_G$ are vesicle radius and polymer radius of gyration respectively. Also the polymer capture into a spherical budd is studied and possible apparatus for easy capture is suggested.Comment: 14 pages RevTeX, 6 postscript figures, published in Phys. Rev. E 57, 730 (1998

Photoproducts of bacteriorhodopsin mutants: a molecular dynamics study

Molecular dynamics simulations of wild-type bacteriorhodopsin (bR) and of its D85N, D85T, D212N, and Y57F mutants have been carried out to investigate possible differences in the photoproducts of these proteins. For each mutant, a series of 50 molecular dynamics simulations of the photoisomerization and subsequent relaxation process were completed. The photoproducts can be classified into four distinct classes: 1) 13-cis retinal, with the retinal N-H+ bond oriented toward Asp-96; 2) 13-cis retinal, with the N-H+ oriented toward Asp-85 and hydrogen-bonded to a water molecule; 3) 13,14-di-cis retinal; 4) all-trans retinal. Simulations of wild-type bR and of its Y57F mutant resulted mainly in class 1 and class 2 products; simulations of D85N, D85T, and D212N mutants resulted almost entirely in class 1 products. The results support the suggestion that only class 2 products initiate a functional pump cycle. The formation of class 1 products for the D85N, D85T, and D212N mutants can explain the reversal of proton pumping under illumination by blue and yellow light

Binding pathway of retinal to bacterio-opsin: a prediction by molecular dynamics simulations

Formation of bacteriorhodopsin (bR) from apoprotein and retinal has been studied experimentally, but the actual pathway, including the point of entry, is little understood. Molecular dynamics simulations provide a surprisingly clear prediction. A window between bR helices E and F in the transmembrane part of the protein can be identified as an entry point for retinal. Steered molecular dynamics, performed by applying a series of external forces in the range of 200–1000 pN over a period of 0.2 ns to retinal, allows one to extract this chromophore from bR once the Schiff base bond to Lys216 is cleaved. Extraction proceeds until the retinal tail forms a hydrogen bond network with Ala144, Met145, and Ser183 side groups lining the exit/entry window. The manipulation induces a distortion with a fitted root mean square deviation of coordinates (ignoring retinal, water, and hydrogen atoms) of less than 1.9 A by the time the retinal carbonyl reaches the protein surface. The forces needed to extract retinal are due to friction and do not indicate significant potential barriers. The simulations therefore suggest a pathway for the binding of retinal. Water molecules are found to play a crucial role in the binding process