Helical states of nonlocally interacting molecules and their linear stability: geometric approach

The equations for strands of rigid charge configurations interacting nonlocally are formulated on the special Euclidean group, SE(3), which naturally generates helical conformations. Helical stationary shapes are found by minimizing the energy for rigid charge configurations positioned along an infinitely long molecule with charges that are off-axis. The classical energy landscape for such a molecule is complex with a large number of energy minima, even when limited to helical shapes. The question of linear stability and selection of stationary shapes is studied using an SE(3) method that naturally accounts for the helical geometry. We investigate the linear stability of a general helical polymer that possesses torque-inducing non-local self-interactions and find the exact dispersion relation for the stability of the helical shapes with an arbitrary interaction potential. We explicitly determine the linearization operators and compute the numerical stability for the particular example of a linear polymer comprising a flexible rod with a repeated configuration of two equal and opposite off-axis charges, thereby showing that even in this simple case the non-local terms can induce instability that leads to the rod assuming helical shapes.Comment: 34 pages, 9 figure

Hopf's last hope: spatiotemporal chaos in terms of unstable recurrent patterns

Spatiotemporally chaotic dynamics of a Kuramoto-Sivashinsky system is described by means of an infinite hierarchy of its unstable spatiotemporally periodic solutions. An intrinsic parametrization of the corresponding invariant set serves as accurate guide to the high-dimensional dynamics, and the periodic orbit theory yields several global averages characterizing the chaotic dynamics.Comment: Latex, ioplppt.sty and iopl10.sty, 18 pages, 11 PS-figures, compressed and encoded with uufiles, 170 k

Comment on “The role of wetting heterogeneities in the meandering instability of a partial wetting rivulet” by Couvreur S. and Daerr A.

Rivulets and their meandering on a partially wetting surface present an interesting problem, as complex behavior arises from a deceptively simple setup. Recently Couvreur and Daerr suggested that meandering is caused by an instability developing as the flow rate $Q$ increases to a critical value $Q_c$, with stationary (pinned) meandering being the final state of the flow. We tried to verify this assertion experimentally, but instead produced results contradicting the claim of Couvreur and Daerr. The likely reason behind the discrepancy is the persistence of flow-rate perturbations. Moreover, the theory presented in this paper cannot reproduce the states as considered and disagrees with other theories

Family 1 Glycosyltransferase UGT706F8 from Zea mays Selectively Catalyzes the Synthesis of Silibinin 7-O-β-d -Glucoside

Regioselective glycosylation is a chemical challenge, leading to multistep syntheses with protecting group manipulations, ultimately resulting in poor atom economy and compromised sustainability. Enzymes allow eco-friendly and regioselective bond formation with fully deprotected substrates in a single reaction. For the selective glucosylation of silibinin, a pharmaceutical challenged with low solubility, enzyme engineering has previously been employed, but the resulting yields and k$_{cat}$ were limited, prohibiting the application of the engineered catalyst. Here, we identified a naturally regioselective silibinin glucosyltransferase, UGT706F8, a family 1 glycosyltransferase from Zea mays. It selectively and efficiently (k$_{cat}$ = 2.1 ± 0.1 s$^{–1}$; KM = 36.9 ± 5.2 $μ$M; TTN = 768 ± 22) catalyzes the quantitative synthesis of silibinin 7-O-β-d-glucoside. We solved the crystal structure of UGT706F8 and investigated the molecular determinants of regioselective silibinin glucosylation. UGT706F8 was the only regioselective enzyme among 18 glycosyltransferases found to be active on silibinin. We found the temperature optimum of UGT706F8 to be 34 °C and the pH optimum to be 7–8. Our results indicate that UGT706F8 is an efficient silibinin glycosyltransferase that enables biocatalytic production of silbinin 7-O-β-d-glucoside

Family 1 Glycosyltransferase UGT706F8 from <i>Zea mays</i> Selectively Catalyzes the Synthesis of Silibinin 7-<i>Ο</i>-<i>β</i>-D-Glucoside

Regioselective glycosylation is a chemical challenge, leading to multistep syntheses with protecting group manipulations, ultimately resulting in poor atom economy and compromised sustainability. Enzymes allow eco-friendly and regioselective bond formation with fully deprotected substrates in a single reaction. For the selective glucosylation of silibinin, a pharmaceutical challenged with low solubility, enzyme engineering has previously been employed, but the resulting yields and k$_{cat}$ were limited, prohibiting the application of the engineered catalyst. Here, we identified a naturally regioselective silibinin glucosyltransferase, UGT706F8, a family 1 glycosyltransferase from Zea mays. It selectively and efficiently (k$_{cat}$ = 2.1 ± 0.1 s$^{–1}$; KM = 36.9 ± 5.2 $μ$M; TTN = 768 ± 22) catalyzes the quantitative synthesis of silibinin 7-O-β-d-glucoside. We solved the crystal structure of UGT706F8 and investigated the molecular determinants of regioselective silibinin glucosylation. UGT706F8 was the only regioselective enzyme among 18 glycosyltransferases found to be active on silibinin. We found the temperature optimum of UGT706F8 to be 34 °C and the pH optimum to be 7–8. Our results indicate that UGT706F8 is an efficient silibinin glycosyltransferase that enables biocatalytic production of silbinin 7-O-β-d-glucoside