On the stability of Hamiltonian systems with weakly time dependent potentials.

We show here that a recently developed criterion for the stability of conservative Hamiltonian systems can be extended to Hamiltonians with weak time dependence. In this method, the geodesic equations contain the Hamilton equations of the original potential model through an inverse map in the tangent space in terms of a geometric embedding. The second covariant derivative of the geodesic deviation generates a dynamical curvature, resulting in a (energy dependent) local criterion for unstable behavior different from the usual Lyapunov criterion. We show by direct simulation that our geometrical criterion predicts correctly the stability/instability of motions, sometimes contrary to indications of the local Lyapunov method.

Space-frequency model of ultrawide-band interactions in free-electron lasers.

The principle of operation of intense radiation devices such as microwave tubes, free-electron lasers, and masers, is based on a distributed interaction between an electron beam and electromagnetic radiation. Some of the effects emerging during the interaction involve a continuum of frequencies in their broadband spectrum. We developed a three-dimensional, space-frequency theory for the analysis and simulation of radiation excitation and propagation in electron devices and free-electron lasers operating in an ultrawide range of frequencies. The total electromagnetic field (radiation and space-charge waves) is presented in the frequency domain as an expansion in terms of transverse eigenmodes of the (cold) cavity, in which the field is excited and propagates. The mutual interaction between the electron beam and the electromagnetic field is fully described by coupled equations, expressing the evolution of mode amplitudes and electron beam dynamics. The approach is applied in a numerical particle code WB3D, simulating wideband interactions in free-electron lasers operating in the linear and nonlinear regimes.

The Arabidopsis homologue of an eIF3 complex subunit associates with the COP9 complex.

The Arabidopsis COP9 complex is a multi-subunit repressor of photomorphogenesis which is conserved among multicellular organisms. Approximately 12 proteins copurify with the COP9 complex. Seven of these proteins are orthologues of subunits of the recently published mammalian COP9 complex. Four of the proteins show amino acid similarity to various subunits of the COP9 complex, eIF3 complex and 19S cap of the proteasome. We have studied one of these proteins in order to determine if it is a component of the COP9 complex. Arabidopsis p105 is highly similar to the p110 subunit of the human elF3. The p105 gene is induced during photomorphogenesis, and RNA and protein analysis reveal different tissue accumulation patterns. p105 is found in a large protein complex. p105 interacts in yeast with both COP9 and FUS6, two known components of the COP9 complex. Our results indicate that p105 is not a component of the COP9 core complex, though it may interact with components of the complex.

Variational procedure for time-dependent processes.

A simple variational Lagrangian is proposed for the time development of an arbitrary density matrix, employing the "factorization" of the density. Only the "kinetic energy" appears in the Lagrangian. The formalism applies to pure and mixed state cases, the Navier-Stokes equations of hydrodynamics, transport theory, etc. It recaptures the least dissipation function condition of Rayleigh-Onsager and in practical applications is flexible. The variational proposal is tested on a two-level system interacting that is subject, in one instance, to an interaction with a single oscillator and, in another, that evolves in a dissipative mode.

A Kinetic Analysis of Phytochrome Controlled Mesocotyl Growth in Zea mays Seedlings.

Mesocotyl elongation in 4 day old etiolated seedlings immediately following 3 hours of white light (3 h W) is reversibly controlled by phytochrome. Time-lapse video measurements were made of the 5 millimeter zone just below the coleoptile which is the main growth region of the mesocotyl. The growth kinetics were determined for five contiguous 1 millimeter zones subtending the coleoptile node for nonirradiated seedlings, for seedlings given 3 h W, and 3 h W followed by terminal far-red (FR) or red subsequent to the far-red (FR/R) irradiation. Each zone in nonirradiated seedlings exhibits exponential elongation kinetics during the early stages of elongation. This finding suggests that during elongation, a growth limiting factor is also exponentially increasing. Following 3 h W differences in the kinetic responses were found for each zone. In all zones, the inhibitory effect following the 3 h W is totally FR reversible. The effect of FR is reversed by R. The upper zone exhibits the fastest response and is the most plastic in its growth response. The three upper zones all exhibit spontaneous and sharp recoveries with time. It is suggested that the control by phytochrome is not inductive but rather continuous, the controlling factor being either the level of the far red-absorbing form of phytochrome (Pfr) or the ratio Pfr to total phytochrome.

Arabidopsis eIF3e (INT-6) associates with both eIF3c and the COP9 signalosome subunit CSN7.

The Arabidopsis COP9 signalosome is a multisubunit repressor of photomorphogenesis that is conserved among eukaryotes. This complex may have a general role in development. As a step in dissecting the biochemical mode of action of the COP9 signalosome, we determined the sequence of proteins that copurify with this complex. Here we describe the association between components of the COP9 signalosome (CSN1, CSN7, and CSN8) and two subunits of eukaryotic translation initiation factor 3 (eIF3), eIF3e (p48, known also as INT-6) and eIF3c (p105). To obtain a biochemical marker for Arabidopsis eIF3, we cloned the Arabidopsis ortholog of the eIF3 subunit eIF3b (PRT1). eIF3e coimmunoprecipitated with CSN7, and eIF3c coimmunoprecipitated with eIF3e, eIF3b, CSN8, and CSN1. eIF3e directly interacted with CSN7 and eIF3c. However, eIF3e and eIF3b cofractionated by gel filtration chromatography in a complex that was larger than the COP9 signalosome. Whereas eIF3, as detected through eIF3b, localized solely to the cytoplasm, eIF3e, like CSN7, was also found in the nucleus. This suggests that eIF3e and eIF3c are probably components of multiple complexes and that eIF3e and eIF3c associate with subunits of the COP9 signalosome, even though they are not components of the COP9 signalosome core complex. This interaction may allow for translational control by the COP9 signalosome.

Maize mesocotyl plasmodesmata proteins cross-react with connexin gap junction protein antibodies.

Polypeptide present in various cell fractions obtained from homogenized maize mesocotyls were separated by sodium dodecyl sulfate-polyacrylamide gel electrophoresis, immunoblotted, and screened for cross-reactivity with antibodies against three synthetic polypeptides spanning different regions of the rat heart gap junctional protein connexin43 and the whole mouse liver gap junctional protein connexin32. An antibody raised against a cytoplasmic loop region of connexin43 cross-reacted strongly with a cell wall-associated polypeptide (possibly a doublet) of 26 kilodaltons. Indirect immunogold labeling of thin sections of mesocotyl tissue with this antibody labeled the plasmodesmata of cortical cells along the entire length of the plasmodesmata, including the neck region and the cytoplasmic annulus. Sections labeled with control preimmune serum were essentially free of colloidal gold. An antibody against connexin32 cross-reacted with a 27-kilodalton polypeptide that was present in the cell wall and membrane fractions. Indirect immunogold labeling of thin sections with this antibody labeled the plasmodesmata mainly in the neck region. It is suggested that maize mesocotyl plasmodesmata contain at least two different proteins that have homologous domains with connexin proteins.