Totally geodesic boundaries of knot complements

Given a compact orientable -manifold whose boundary is a hyperbolic surface and a simple closed curve in its boundary, every knot in is homotopic to one whose complement admits a complete hyperbolic structure with totally geodesic boundary in which the geodesic representative of is as small as you like.

     

Absolute quantitation of host cell proteins in recombinant human monoclonal antibodies with an automated CZE‐ESI‐MS/MS system

We report the first use of CZE for absolute characterization of host cell proteins (HCPs) in recombinant human monoclonal antibodies. An electrokinetically pumped nanoelectrospray interface was used to couple CZE with a tandem mass spectrometer. Three isotopic‐labeled peptides (LSFDKDAMVAR, VDIVENQAMDTR, and LVSDEMVVELIEK) were synthesized by direct incorporation of an isotope‐labeled lysine or arginine. The heavy‐labeled peptides were spiked in the HCP digests at known concentrations. After CZE‐ESI‐MS/MS analysis, the peaks of native and isotopic‐labeled peptides were extracted with mass tolerance ≤ 5 ppm from the electropherograms, and the ratios of peak area between native and isotopic‐labeled peptides pairs were calculated. Calibration curves (the ratios of peak area versus spiked peptide amount) with R² values of 0.999, 0.997, and 0.999 were obtained for the three HCP peptides, and the absolute amounts of the three proteins present were determined to be at the picomole level in a 20 μg sample of digested HCPs. The target proteins were present at the 7–30 ppt level in the purified HCP samples.     

A charge iteration-corrected extended-Hückel study of the electronic and spectroscopic properties of conjugated heterocycles

A computationally inexpensive modified extended-Hückel method using coordinates from STO-6G(d,p) geometry optimizations is described and shown to accurately simulate the spectra of conjugated heterocycles. The origins of the natural optical activities of blue indophenines and diheptylindophenines, and several related brown, red, and colorless compounds, were investigated with this method to show how it can be used to examine the changes in spectra and electronic structure that occur with substituent additions and changes. Diheptylindophenines were found to be blue because of absorptions from electronic transitions between spatially congruent π and π* molecular orbitals delocalized across carbon, nitrogen, oxygen, and sulfur atomic orbitals. The effects of conjugated thiophene moieties replacing the isatin moiety β-carbonyls move these absorptions to the blue relative to their locations in n-heptylisatin, and the diheptyl groups move these absorptions slightly to the red relative to indophenines.     

Capillary zone electrophoresis tandem mass spectrometry detects low concentration host cell impurities in monoclonal antibodies

We have evaluated CZE‐ESI‐MS/MS for detection of trace amounts of host cell protein impurities in recombinant therapeutics. Compared to previously published procedures, we have optimized the buffer pH used in the formation of a pH junction to increase injection volume. We also prepared a 5‐point calibration curve by spiking 12 standard proteins into a solution of a human mAb. A custom CZE‐MS/MS system was used to analyze the tryptic digest of this mixture without depletion of the antibody. CZE generated a ～70‐min separation window (～90‐min total analysis duration) and ～300‐peak capacity. We also analyzed the sample using ultra‐performance LC‐MS/MS. CZE‐MS/MS generated approximately five times higher base peak intensity and more peptide identifications for low‐level spiked proteins. Both methods detected all proteins spiked at ～100 ppm level with respect to the antibody.     

Comparing normal modes across different models and scales: Hessian reduction versus coarse‐graining

Dimension reduction is often necessary when attempting to reach longer length and time scales in molecular simulations. It is realized by constraining degrees of freedom or by coarse‐graining the system. When evaluating the accuracy of a dimensional reduction, there is a practical challenge: the models yield vectors with different lengths, making a comparison by calculating their dot product impossible. This article investigates mapping procedures for normal mode analysis. We first review a horizontal mapping procedure for the reduced Hessian techniques, which projects out degrees of freedom. We then design a vertical mapping procedure for the “implosion” of the all‐atom (AA) Hessian to a coarse‐grained scale that is based upon vibrational subsystem analysis. This latter method derives both effective force constants and an effective kinetic tensor. Next, a series of metrics is presented for comparison across different scales, where special attention is given to proper mass‐weighting. The dimension‐dependent metrics, which require prior mapping for proper evaluation, are frequencies, overlap of normal mode vectors, probability similarity, Hessian similarity, collectivity of modes, and thermal fluctuations. The dimension‐independent metrics are shape derivatives, elastic modulus, vibrational free energy differences, heat capacity, and projection on a predefined basis set. The power of these metrics to distinguish between reasonable and unreasonable models is tested on a toy alpha helix system and a globular protein; both are represented at several scales: the AA scale, a Gō‐like model, a canonical elastic network model, and a network model with intentionally unphysical force constants. Published 2012 Wiley Periodicals, Inc.     

Geometric limits of knot complements, II: graphs determined by their complements

We prove that there are compact submanifolds of the 3-sphere whose interiors are not homeomorphic to any geometric limit of hyperbolic knot complements.     

In Situ Formation of Gold Nanoparticles within a Polymer Particle and Their Catalytic Activities in Various Chemical Reactions

Composite materials consisting of nanoscale gold particles and protective polymer shells were designed and tested as catalysts in various chemical reactions. Initially, the systematic incorporation of multiple gold nanoparticles into a poly(N-isopropylacrylamide) particle was achieved by an in situ method under light irradiation. The degree of gold nanoparticle loading, along with the structural and morphological properties, was examined as a function of the amount of initial gold ions and reducing agent. As these gold nanoparticles were physically-embedded within the polymer particle in the absence of strong interfacial interactions between the gold nanoparticles and polymer matrix, the readily-accessible surface of the gold nanoparticles with a highly increased stability allowed for their use as recyclable catalysts in oxidation, reduction, and coupling reactions. Overall, the ability to integrate catalytically-active metal nanoparticles within polymer particles in situ allows for designing novel composite materials for multi-purpose catalytic systems.     

Synthesis,Structural, and Optical Characterization of a New Europium(II) Tin Selenide,Eu8(Sn4Se14)(Se3)2 with a (Sn4Se14)12– Building Block

A new phase in europium‐tin‐chalcogenide chemistry has been prepared using the reactive flux method: Eu₈(Sn₄Se₁₄)(Se₃)₂. The compound crystallizes in the orthorhombic space group P2₁2₁2 with cell parameters a = 11.990(2) Å, b = 16.425(4) Å, c = 8.543(1) Å, and Z = 2. Eu₈(Sn₄Se₁₄)(Se₃)₂ is a three dimensional structure with Eu^II cations linked together with an unusual (Sn₄Se₁₄)^12– anionic unit and (Se₃)^2– chains. UV‐VIS‐NIR band‐gap analysis shows that these black metallic crystals are likely semiconductors with an optical band‐gap of 1.07 eV.     

Double-walled pyr topology networks from a novel fluoride-bridged heptanuclear metal cluster

Two isostructural metal–organic materials, Tripp-1-M (Tripp = 2,4,6-tris(4-pyridyl)pyridine; M = Co, Ni), that exhibit binodal 3,6-connected pyr network topology have been prepared and characterized. Tripp-1-M are based upon a novel M₇F₁₂ ²⁺ cluster that possesses 12 connection points but, because of double cross-linking by 3-connected Tripp ligands, it functions as a 6-connected supermolecular building block (SBB).     

Theory of photon statistics in single-molecule Förster resonance energy transfer

We present the theory for the distribution of the number of donor and acceptor photons detected in a time bin and the corresponding energy-transfer efficiency distribution obtained from single-molecule Forster resonance energy-transfer measurements. Photon counts from both immobilized and freely diffusing molecules are considered. Our starting point is the joint distribution for the donor and acceptor photons for a system described by an arbitrary kinetic scheme. This is simplified by exploiting the time scale separation between fast fluorescent transitions and slow processes which include conformational dynamics, intersystem conversion to a dark state, and translational diffusion in and out of the laser spot. The fast fluorescent transitions result in a Poisson distribution of the number of photons which is then averaged over slow fluctuations of the local transfer efficiency and the total number of photons. The contribution of various processes to the distribution and the variance of the energy-transfer efficiency are analyzed.