On the van der Waerden conjecture and zeros of polynomials

Let

$\text{F(x) =}\text{∑}\text{k=o}\text{n}\text{n}\text{k}\text{A}{}_{\mathrm{k}}\text{x}{}^{\mathrm{k}}$

$\text{A}{}_{\mathrm{n}}\text{≠ 0,}$

and

$\text{G(x) =}\text{∑}\text{k=o}\text{n}\text{n}\text{k}\text{B}{}_{\mathrm{k}}\text{x}{}^{\mathrm{k}}$

$\text{B}{}_{\mathrm{n}}\text{≠ 0,}$

be polynomials with real zeros satisfying A_n?1 = B_n?1 = 0, and let

$\text{H(x) =}\text{∑}\text{k=o}\text{n-2}\text{n}\text{k}\text{A}{}_{\mathrm{k}}\text{B}{}_{\mathrm{k}}\text{x}{}^{\mathrm{k}}\text{.}$

Using the recently proved validity of the van der Waerden conjecture on permanents, some results on the real zeros of H(x) are obtained. These results are related to classical results on composite polynomials.     

Theoretical analysis of the inter-ligand overhauser effect: a new approach for mapping structural relationships of macromolecular ligands

A theoretical framework has been developed for the evaluation of inter-ligand Overhauser effects (ILOE), predicted when pairs of ligands are observed in the presence of a macromolecular receptor which can form a ternary complex such that some of the protons on the two ligands are in close proximity with each other (generally less than approximately 5 A). Simulations for a pair of ligands with three spins each have been performed for a variety of geometric and rate parameters. Analogous to previously described calculations of TRNOE behavior, theoretical behavior of each of the nine cross peaks, A(ij), in a NOESY experiment involving ligands which can exist in the free, binary, or ternary complex states can be calculated. However, for exchange which is sufficiently rapid on the relaxation and chemical shift time scales, use of a collapsed matrix, C, corresponding to sums of sets of nine elements, will often be appropriate and generally simplifies the analysis. In order to generate inter-ligand Overhauser effects, it is optimal for the fraction of receptor involved in the ternary complex to be reasonably large; i.e., concentrations of both ligands should be near saturation. Based on a model assuming random binding order of the ligands, the dependence of ILOE resonance intensities on kinetic rate constants roughly parallels the dependence of transferred NOE (TRNOE) intensities. For diffusion controlled binding, i.e., k(on) approximately 10(8) M(-1) s(-1), the method is best suited for equilibrium dissociation constants in the micromolar-millimolar range (k(off) approximately 10(2)-10(5) s(-1)). Toward the slower dissociation rate constant end of this range, TRNOE and ILOE effects are still predicted, but the initial build-up curves become markedly nonlinear. For a kinetic binding scheme which assumes ordered binding of the ligands, the inherent asymmetry of the ligand binding process leads to more complex kinetics and alters the dependence of the ILOE on the kinetic parameters. In this case, the binding of the second ligand effectively reduces the exchange rate of the first ligand, reducing the transfer of NOE and ILOE information. The reduction in TRNOE and ILOE information which is prediced for the ordered ligand binding model is overcome at larger dissociation rate constants for either ligand 1 or ligand 2. In addition to the structural information available from ILOE data, the strong dependence of TRNOE and ILOE curves on ordered ligand binding suggests that such measurements could be useful for the characterization of ligand binding kinetics.     

Dependence of amino acid side chain 13C shifts on dihedral angle: application to conformational analysis

Chemical shift data from the BiomagResDataBank and conformational data derived from the protein data bank have been correlated in order to explore the conformational dependence of side chain (13)C resonance shifts. Consistent with predictions based on steric compression, upfield shifts for Cgamma resonances of Thr, Val, Ile, Leu, Met, Arg, Lys, Glu, and Gln residues correlate with both the number of heavy atom (nonproton) gamma-substituents and with gauche conformational orientations of gamma-substituents. The (13)C shift/conformation correlations are most apparent for Cgamma carbons but also can be observed at positions further from the backbone. Intraresidue steric conflict leads to a correlation between upfield-shifted side chain (13)C resonances and statistically lower probabilities in surveys of protein side chain conformation. Illustrative applications to the DNA pol lambda lyase domain and to dihydrofolate reductase are discussed. In the latter case, (13)C shift analysis indicates that the conformation of the remote residue V119 on the betaF-betaG loop is correlated with the redox state of the bound pyridine nucleotide cofactor, providing one basis for discrimination between substrate and product. It is anticipated that (13)C shift data for protein sidechains can provide a useful basis for the analysis of conformational changes even in large, deuterated proteins. Additionally, the large dependence of the leucine methyl shift difference, deltaCdelta1-deltaCdelta2, on both chi1 and chi2 is sufficient to allow this parameter to be used as a restraint in structure calculations if stereospecific assignment data are available.     

Large-scale molecular dynamics simulations of dense plasmas: The Cimarron Project

We describe the status of a new time-dependent simulation capability for dense plasmas. The backbone of this multi-institutional effort – the Cimarron Project – is the massively parallel molecular dynamics (MD) code “ddcMD,” developed at Lawrence Livermore National Laboratory. The project’s focus is material conditions such as exist in inertial confinement fusion experiments, and in many stellar interiors: high temperatures, high densities, significant electromagnetic fields, mixtures of high- and low-Z elements, and non-Maxwellian particle distributions. Of particular importance is our ability to incorporate into this classical MD code key atomic, radiative, and nuclear processes, so that their interacting effects under non-ideal plasma conditions can be investigated. This paper summarizes progress in computational methodology, discusses strengths and weaknesses of quantum statistical potentials as effective interactions for MD, explains the model used for quantum events possibly occurring in a collision, describes two new experimental efforts that play a central role in our validation work, highlights some significant results obtained to date, outlines concepts now being explored to deal more efficiently with the very disparate dynamical timescales that arise in fusion plasmas, and provides a careful comparison of quantum effects on electron trajectories predicted by more elaborate dynamical methods.     

Rationally designed macrocyclic peptides as synergistic agonists of LPS-induced inflammatory response

Toll-like receptor 4 (TLR4) plays an important role in the regulation of the innate and adaptive immune response. Both agonists and antagonists of TLR4 are of considerable interest as drug leads for various disease indications. We herein report the rational design of two myeloid differentiation factor 2 (MD2)-derived macrocyclic peptides as TLR4 modulators, using the Rosetta Macromolecular Modeling software. The designed cyclic peptides, but not their linear counterparts, displayed synergistic activation of TLR signaling when co-administered with lipopolysaccharide (LPS). Although the understanding of the mechanism of action of these peptides remains elusive, these results underscore the utility of peptide cyclization for the discovery of biologically active agents, and also provide valuable tools for the investigation of TLR4 signaling.     

Subnanometer-scale measurements of the interaction of ultrafast soft x-ray free-electron-laser pulses with matter

At the recently built FLASH x-ray free-electron laser, we studied the reflectivity of Si/C multilayers with fluxes up to 3 x 10(14) W/cm2. Even though the nanostructures were ultimately completely destroyed, we found that they maintained their integrity and reflectance characteristics during the 25-fs-long pulse, with no evidence for any structural changes over lengths greater than 3 A. This experiment demonstrates that with intense ultrafast pulses, structural damage does not occur during the pulse, giving credence to the concept of diffraction imaging of single macromolecules.