A Markov Model of Production, Trade, and Money: Theory and Artificial Life Simulation

The paper generalizes the Kiyotaki-Wright trade model by treatingthe trading period as a finite game, so Nash's theorem can be used to provethe existence of equilibrium, and by treating the economy as a Markovprocess, so an ergodic theorem can be used to show the existence ofequilibria with desirable properties (e.g., in which money exists). A Markovmodel of trade also allows us to add complexity to the economy withoutadding corresponding complexity to the analysis of the model's properties.The paper also provides artificial life simulations of the Markov economysuggesting that monetary equilibria are dynamically stable and do notrequire high levels of learning or information processing on the part ofagents.     

Tracer diffusion in lattice gases

It has been proved that a tracer particle in a reversible lattice gas converges to Brownian motion. However, only in a few particular cases has a strictly positive self-diffusion coefficientD been established. Here we supply the missing piece and show thatD>0 in general. The exceptions are one-dimensional lattice gases with nearest neighbor jumps only, for whichD=0. The proof establishes a variational formula forD which could be used to obtain realistic bounds.     

On optimal regularity of free boundary problems and a conjecture of De Giorgi

We present a general theory to study optimal regularity for a large class of nonlinear elliptic systems satisfying general boundary conditions and in the presence of a geometric transmission condition on the free boundary. As an application we give a full positive answer to a conjecture of De Giorgi on the analyticity of local minimizers of the Mumford‐Shah functional. © 2004 Wiley Periodicals, Inc.     

Generating Metallic Amorphous Core–Shell Nanoparticles by a Solid‐State Amorphization Process

Metallic crystalline/amorphous core–shell nanoparticles consisting of a crystalline Pd core (c‐Pd) surrounded by an amorphous Fe₂₅Sc₇₅ shell (a‐FeSc) are prepared by inert‐gas condensation. A phase transformation of the c‐Pd by a solid‐state diffusion process resulting in an amorphous core (a‐PdSc) surrounded by an amorphous FeSc shell is observed if the core–shell structure is irradiated at ambient temperature with 300 keV electrons. The amorphization process seems to involve the diffusion of irradiation‐induced defects and is presumably driven by the large negative heat of mixing of Pd and Sc, as well as by the excess enthalpy of the interfaces between the c‐Pd regions and the surrounding a‐FeSc. The structural transformation reported here opens a new way to producing metallic amorphous core–shell nanoparticles of different chemical compositions and probably novel properties.     

Trans-cis isomerization is responsible for the red-shifted fluorescence in variants of the red fluorescent protein eqFP611

An important class of red fluorescent proteins (RFPs) feature a 2-iminomethyl-5-(4-hydroxybenzylidene)imidazolinone chromophore. Among these proteins, eqFP611 has the chromophore in a coplanar trans orientation, whereas the cis isomer is preferred by other RFPs such as DsRed and its variants. In the photoactivatable protein asFP595, the chromophore can even be switched from the nonfluorescent trans to the fluorescent cis state by light. By using X-ray crystallography, we have determined the structure of dimeric eqFP611 at high resolution (up to 1.1 A). In the far-red emitting eqFP611 variant d2RFP630, which carries an additional Asn143Ser mutation, the chromophore resides predominantly (approximately 80%) in the cis isomeric state, and in RFP639, which has Asn143Ser and Ser158Cys mutations, the chromophore is found completely in the cis form. The pronounced red shift of excitation and emission maxima of RFP639 can thus unambiguously be assigned to trans-cis isomerization of the chromophore. Among RFPs, eqFP611 is thus unique because its chromophore is highly fluorescent in both the cis and trans isomeric forms.     

The lipidated membrane anchor of full length N-Ras protein shows an extensive dynamics as revealed by solid-state NMR spectroscopy

Many proteins involved in signal transduction are equipped with covalently attached lipid chains providing a hydrophobic anchor targeting these molecules to membranes. Despite the considerable biological significance of this membrane binding mechanism for 5-10% of all cellular proteins, to date very little is known about structural and dynamical features of lipidated membrane binding domains. Here we report the first comprehensive study of the molecular dynamics of the C-terminus of membrane-associated full-length lipidated Ras protein determined by solid-state NMR. Fully functional lipid-modified N-Ras protein was obtained by chemical-biological synthesis ligating the expressed water soluble N-terminus with a chemically synthesized (2)H or (13)C labeled lipidated heptapeptide. Dynamical parameters for the lipid chain modification at Cys 181 were determined from static (2)H NMR order parameter and relaxation measurements. Order parameters describing the amplitude of motion in the protein backbone and the side chain were determined from site-specific measurements of (1)H-(13)C dipolar couplings for all seven amino acids in the membrane anchor of Ras. Finally, the correlation times of motion were determined from temperature dependent relaxation time measurements and analyzed using a modified Lipari Szabo approach. Overall, the C-terminus of Ras shows a versatile dynamics with segmental fluctuations and axially symmetric overall motions on the membrane surface. In particular, the lipid chain modifications are highly flexible in the membrane.