Diazotrifluoropropionamido-containing prenylcysteines: syntheses and applications for studying isoprenoid-protein interactions

Photoaffinity-labeled prenylcysteines (1 and 2) incorporating a diazotrifluoropropionamide-based photophore have been prepared. Photolyses of 2 in the presence of RhoGDI, a protein that interacts with prenylated proteins, and prenylcysteine-containing competitors demonstrate the effectiveness of this photoaffinity-labeled analogue as a tool for studying isoprenoid binding sites.     

Bicyclo[5.3.1]undec-1(10)-ene bridgehead olefin stability and the taxane bridgehead olefin

MM2 calculations have shown how substituent and conformational effects play a role in the stabilities of systems containing the bicyclo[5.3.1]undec-I(10)-ene moiety and that the taxane diterpene skeleton which possesses this structural feature is surprisingly stable.     

Geometry and entropy of generalized rotation sets

For a continuous map f on a compact metric space we study the geometry and entropy of the generalized rotation set Rot(Φ). Here Φ = (?₁, ..., ? _m ) is a m-dimensional continuous potential and Rot(Φ) is the set of all µ-integrals of Φ and µ runs over all f-invariant probability measures. It is easy to see that the rotation set is a compact and convex subset of ? ^m . We study the question if every compact and convex set is attained as a rotation set of a particular set of potentials within a particular class of dynamical systems. We give a positive answer in the case of subshifts of finite type by constructing for every compact and convex set K in ? ^m a potential Φ = Φ(K) with Rot(Φ) = K. Next, we study the relation between Rot(Φ) and the set of all statistical limits Rot _Pt (Φ). We show that in general these sets differ but also provide criteria that guarantee Rot(Φ) = Rot _Pt (Φ). Finally, we study the entropy function w ? H(w),w ∈ Rot(Φ). We establish a variational principle for the entropy function and show that for certain non-uniformly hyperbolic systems H(w) is determined by the growth rate of those hyperbolic periodic orbits whose Φ-integrals are close to w. We also show that for systems with strong thermodynamic properties (sub-shifts of finite type, hyperbolic systems and expansive homeomorphisms with specification, etc.) the entropy function w ? H(w) is real-analytic in the interior of the rotation set.