Covering dimension and finite-to-one maps

Hurewicz characterized the dimension of separable metrizable spaces by means of finite-to-one maps. We investigate whether this characterization also holds in the class of compact F-spaces of weight c. Our main result is that, assuming the Continuum Hypothesis, an n-dimensional compact F-space of weight c is the continuous image of a zero-dimensional compact Hausdorff space by an at most n²-to-1 map.     

Proton transfer events in GFP

Proton transfer is one of the most important elementary processes in biology. Green fluorescent protein (GFP) serves as an important model system to elucidate the mechanistic details of this reaction, because in GFP proton transfer can be induced by light absorption. Illumination initiates proton transfer through a 'proton-wire', formed by the chromophore (the proton donor), water molecule W22, Ser205 and Glu222 (the acceptor), on a picosecond time scale. To obtain a more refined view of this process, we have used a combined approach of time resolved mid-infrared spectroscopy and visible pump-dump-probe spectroscopy to resolve with atomic resolution how and how fast protons move through this wire. Our results indicate that absorption of light by GFP induces in 3 ps (10 ps in D(2)O) a shift of the equilibrium positions of all protons in the H-bonded network, leading to a partial protonation of Glu222 and to a so-called low barrier hydrogen bond (LBHB) for the chromophore's proton, giving rise to dual emission at 475 and 508 nm. This state is followed by a repositioning of the protons on the wire in 10 ps (80 ps in D(2)O), ultimately forming the fully deprotonated chromophore and protonated Glu222.     

Level sets of signed Takagi functions

This paper examines level sets of functions of the form $$ f(x)=\sum_{n=0}^\infty \frac{r_n}{2^n}\phi(2^n x), $$ where $\phi(x)=\operatorname{dist}\, (x,\mathbb {Z})$ , the distance from x to the nearest integer, and r _n =±1 for each n. Such functions are referred to as signed Takagi functions. The case when r _n =1 for all n is the classical Takagi function, a well-known example of a continuous but nowhere differentiable function. For f of the above form, the maximum and minimum values of f are expressed in terms of the sequence {r _n }. It is then shown that almost all level sets of f are finite (with respect to Lebesgue measure on the range of f), but the set of ordinates y with an uncountably large level set is residual in the range of f. The concept of a local level set of the Takagi function, due to Lagarias and Maddock, is extended to arbitrary signed Takagi functions. It is shown that the average number of local level sets contained in a level set of f is the reciprocal of the height of the graph of f, and consequently, this average lies between 3/2 and 2. These results generalize recent findings by Buczolich [8], Lagarias and Maddock [14], and Allaart [3].     

Interplay Between J‐ and H‐Type Coupling in Aggregates of π‐Conjugated Polymers: A Single‐Molecule Perspective

Strong dipole–dipole coupling within and between π‐conjugated segments shifts electronic transitions, and modifies vibronic coupling and excited‐state lifetimes. Since J‐type coupling between monomers along the conjugated‐polymer (CP) chain and H‐type coupling of chromophores between chains of a CP compete, a superposition of the spectral modifications arising from each type of coupling emerges, making the two couplings hard to discern in the ensemble. We introduce a single‐molecule H‐type aggregate of fixed spacing and variable length of up to 10 nm. HJ‐type aggregate formation is visualized intuitively in the scatter of single‐molecule spectra.     

Crosslinking index,molar mass distribution and rubber equilibrium shear modulus during polyfunctional crosslinking: Part II: Application to real systems

In a previous paper a theory was presented concerning gels formed by polyfunctional crosslinks in a polydisperse primary polymer. The equilibrium shear modulus as well as the crosslinking index were obtained as functions of the functionality of the crosslinks and of the sol fraction. In this paper the theory is applied to gelatin gels (known functionality of crosslinks) and to poly(vinyl chloride) gels (known number of crosslinks).     

Triazolinedione protein modification: from an overlooked off-target effect to a tryptophan-based bioconjugation strategy

Labelling of tyrosine residues in peptides and proteins has been reported to selectively occur via a ‘tyrosine-click’ reaction with triazolinedione reagents (TAD). However, we here demonstrate that TAD reagents are actually not selective for tyrosine and that tryptophan residues are in fact also labelled with these reagents. This off-target labelling remained under the radar as it is challenging to detect these physiologically stable but thermally labile modifications with the commonly used HCD and CID MS/MS techniques. We show that selectivity of tryptophan over tyrosine can be achieved by lowering the pH of the aqueous buffer to effect selective Trp-labelling. Given the low relative abundance of tryptophan compared to tyrosine in natural proteins, this results in a new site-selective bioconjugation method that does not rely on enzymes nor unnatural amino acids and is demonstrated for peptides and recombinant proteins.

A new strategy for selective tryptophan modification using triazolinedione (TAD) chemistry at pH 4 is shown on peptides and proteins. Additionally, off-target modification of tryptophan residues during the classical TAD-Y click reaction is uncovered.     

Microscopic approach to magnetic excitations in IBM-2

Starting from the collective SD subspace of the shell model, we construct boson images of the hamiltonian and the M1 and M3 operators by using the OAI method. In the magnetic operators one-boson as well as two-boson terms are considered. Energy spectra and g-factors of ^130,134Ba are well reproduced by this method. Relatively strong magnetic dipole and octupole transitions at E_x ～ 2 MeV are predicted. The M1 and M3 electron scattering form factors are calculated. It turns out that the magnetic dipole operator is mainly a one-body operator in boson space, whereas the magnetic octupole operator contains important two-boson terms, which give sizeable contributions to the excitation strengths. These two-boson terms tend to diminish the F-spin selectivity of M3 excitations.