Reduction of symplectic manifolds with symmetry

We give a unified framework for the construction of symplectic manifolds from systems with symmetries. Several physical and mathematical examples are given; for instance, we obtain Kostant’s result on the symplectic structure of the orbits under the coadjoint representation of a Lie group. The framework also allows us to give a simple derivation of Smale's criterion for relative equilibria. We apply our scheme to various systems, including rotationally invariant systems, the rigid body, fluid flow, and general relativity.     

Decomposition of (Co)isotropic Relations

We identify 13 isomorphism classes of indecomposable coisotropic relations between Poisson vector spaces and show that every coisotropic relation between finite-dimensional Poisson vector spaces may be decomposed as a direct sum of multiples of these indecomposables. We also find a list of 13 invariants, each of which is the dimension of a space constructed from the relation, such that the 13-vector of multiplicities and the 13-vector of invariants are related by an invertible matrix over \({\mathbb{Z}}\). It turns out to be simpler to do the analysis above for isotropic relations between presymplectic vector spaces. The coisotropic/Poisson case then follows by a simple duality argument.     

Hydrostatic pressure dependence of negative-donor-ion singlet and singlet-like bound magnetoplasmon transitions in doped GaAs/AlGaAs quantum wells

Applied hydrostatic pressure modifies the Coulomb bound states of a quasi-two-dimensional electron gas in quantum wells by increasing the effective mass and by tuning the free electron density. Here, we explore these mechanisms by measuring the effects of pressure on the cyclotron resonance, the D⁰ 1s → 2p⁺ transition, and the D⁻-singlet and singlet-like transitions in low-and high-density, modulation-doped GaAs quantum wells. For low doping density, detailed calculations employing a pressure-dependent electron mass agree well with the observed magnetic field and pressure dependencies. For high doping density and low fields, the blue-shift of the D⁻-singlet-like transition at fields below 8 T decreases with applied pressure as anticipated, due to loss of free electrons via the Γ–X crossover. However, near 7.5 T, this singlet-like transition exhibits an anomalous branching for pressures above 4 kbar, which indicates the presence of a resonant level and obscures the blue-shift at high fields.     

Simulation of pH-Dependent Conformational Transitions in Membrane Proteins: The CLC-ec1 Cl−/H+ Antiporter

Intracellular transport of chloride by members of the CLC transporter family involves a coupled exchange between a Cl⁻ anion and a proton (H⁺), which makes the transport function dependent on ambient pH. Transport activity peaks at pH 4.5 and stalls at neutral pH. However, a structure of the WT protein at acidic pH is not available, making it difficult to assess the global conformational rearrangements that support a pH-dependent gating mechanism. To enable modeling of the CLC-ec1 dimer at acidic pH, we have applied molecular dynamics simulations (MD) featuring a new force field modification scheme—termed an Equilibrium constant pH approach (ECpH). The ECpH method utilizes linear interpolation between the force field parameters of protonated and deprotonated states of titratable residues to achieve a representation of pH-dependence in a narrow range of physiological pH values. Simulations of the CLC-ec1 dimer at neutral and acidic pH comparing ECpH-MD to canonical MD, in which the pH-dependent protonation is represented by a binary scheme, substantiates the better agreement of the conformational changes and the final model with experimental data from NMR, cross-link and AFM studies, and reveals structural elements that support the gate-opening at pH 4.5, including the key glutamates Glu_in and Glu_ex.     

Nonlocality Without Nonlocality

Bell’s theorem is purported to demonstrate the impossibility of a local “hidden variable” theory underpinning quantum mechanics. It relies on the well-known assumption of ‘locality’, and also on a little-examined assumption called ‘statistical independence’ (SI). Violations of this assumption have variously been thought to suggest “backward causation”, a “conspiracy” on the part of nature, or the denial of “free will”. It will be shown here that these are spurious worries, and that denial of SI simply implies nonlocal correlation between spacelike degrees of freedom. Lorentz-invariant theories in which SI does not hold are easily constructed: two are exhibited here. It is conjectured, on this basis, that quantum-mechanical phenomena may be modeled by a local theory after all. This paper is dedicated to the memory of John A. Wheeler.     

Structural Determination of a Photochemically Active Diplatinum Molecule by Time‐Resolved EXAFS Spectroscopy

Metallica : A large contraction of the Pt? Pt bond in the triplet excited state of the photoreactive [Pt₂(P₂O₅H₂)₄]^4? ion is determined by time‐resolved X‐ray absorption spectroscopy (see picture). The strengthening of the Pt? Pt interaction is accompanied by a weakening of the ligand coordination bonds, resulting in an elongation of the platinum–ligand bond that is determined for the first time.

     

Dynamic models of G-protein coupled receptor dimers: indications of asymmetry in the rhodopsin dimer from molecular dynamics simulations in a POPC bilayer

Based on the growing evidence that G-protein coupled receptors (GPCRs) form homo- and hetero-oligomers, models of GPCR signaling are now considering macromolecular assemblies rather than monomers, with the homo-dimer regarded as the minimal oligomeric arrangement required for functional coupling to the G-protein. The dynamic mechanisms of such signaling assemblies are unknown. To gain some insight into properties of GPCR dimers that may be relevant to functional mechanisms, we study their current structural prototype, rhodopsin. We have carried out nanosecond time-scale molecular dynamics (MD) simulations of a rhodopsin dimer and compared the results to the monomer simulated in the same type of bilayer membrane model composed of an equilibrated unit cell of hydrated palmitoyl-oleoyl-phosphatidyl choline (POPC). The dynamic representation of the homo-dimer reveals the location of structural changes in several regions of the monomeric subunits. These changes appear to be more pronounced at the dimerization interface that had been shown to be involved in the activation process [Proc Natl Acad Sci USA 102:17495, 2005]. The results are consistent with a model of GPCR activation that involves allosteric modulation through a single GPCR subunit per dimer.