An Average-Stretch Full-Network Model for Rubber Elasticity

Two constitutive models that are based on the classical non-Gaussian, Kuhn-Grün probability distribution function are reviewed. It is shown that all chains of a network cell structure comprised of a finite number of identical chains in an affine deformation referred to principal axes may have the same invariant stretch, if and only if the chains are oriented initially along any of eight directions forming the diagonals of a unit cube. The 4-chain tetrahedral and the 8-chain cubic cell structures are familiar admissible models having this property. An easy derivation of the constitutive equation for the Wu and van der Giessen full-network model of initially identical chains arbitrarily oriented in the undeformed state is presented. The constitutive equations for the neo-Hookean model, the 3 -chain model, and the equivalent 4- and 8-chain models are then derived from the Wu and van der Giessen equation. The squared chain stretch of an arbitrarily directed chain averaged over a unit sphere surrounding all chains radiating from a cross-link junction as its center is determined. An average-stretch, full-network constitutive equation is then derived by approximation of the Wu and van der Giessen equation. This result, though more general in that no special chain cell morphology is introduced, is the same as the constitutive equation for the 4- and 8-chain models. Some concluding remarks on extensions to amended models are presented.     

Selective dye-labeling of newly synthesized proteins in bacterial cells

We describe fluorescence labeling of newly synthesized proteins in Escherichia coli cells by means of Cu(I)-catalyzed cycloaddition between alkynyl amino acid side chains and the fluorogenic dye 3-azido-7-hydroxycoumarin. The method involves co-translational labeling of proteins by the non-natural amino acids homopropargylglycine (Hpg) or ethynylphenylalanine (Eth) followed by treatment with the dye. As a demonstration, the model protein barstar was expressed and treated overnight with Cu(I) and 3-azido-7-hydroxycoumarin. Examination of treated cells by confocal microscopy revealed that strong fluorescence enhancement was observed only for alkynyl-barstar treated with Cu(I) and the reactive dye. The cellular fluorescence was punctate, and gel electrophoresis confirmed that labeled barstar was localized in inclusion bodies. Other proteins showed little fluorescence. Examination of treated cells by fluorimetry demonstrated that cultures supplemented with Eth or Hpg showed an 8- to 14-fold enhancement in fluorescence intensity after labeling. Addition of a protein synthesis inhibitor reduced the emission intensity to levels slightly above background, confirming selective labeling of newly synthesized proteins in the bacterial cell.