Copper-induced oligomerization of peptides: a model study

In this work, copper-binding of the tetraglycine peptide (Gly-Gly-Gly-Gly) was studied by electrospray ionization mass spectrometry. Experiments were performed under alkaline conditions, in the presence of ethanolamine (pH 10.95). We observed that the presence of copper(II) ions induces the aggregation of the peptide and the formation of copper-bound complexes with higher molecular mass is favored, such as the oligomer complexes [3M+2Cu-3H](+) and [4M+3Cu-5H](+). At 1:1 peptide-copper(II) ion ratio, the singly charged [3M+2Cu-3H](+) oligomer complex is the base peak in the mass spectrum. Metal ion-induced oligomer-ization of neurotoxic peptides is well known in the literature; however, there are very few examples in which such oligomerization was directly observed by mass spectrometry. Our results show that application of short peptides can be useful to study the -mechanism of metal ion binding and metal ion-induced oligomerization of peptides.     

Robust dimension reduction,fusion frames,and Grassmannian packings

We consider estimating a random vector from its measurements in a fusion frame, in presence of noise and subspace erasures. A fusion frame is a collection of subspaces, for which the sum of the projection operators onto the subspaces is bounded below and above by constant multiples of the identity operator. We first consider the linear minimum mean-squared error (LMMSE) estimation of the random vector of interest from its fusion frame measurements in the presence of additive white noise. Each fusion frame measurement is a vector whose elements are inner products of an orthogonal basis for a fusion frame subspace and the random vector of interest. We derive bounds on the mean-squared error (MSE) and show that the MSE will achieve its lower bound if the fusion frame is tight. We then analyze the robustness of the constructed LMMSE estimator to erasures of the fusion frame subspaces. We limit our erasure analysis to the class of tight fusion frames and assume that all erasures are equally important. Under these assumptions, we prove that tight fusion frames consisting of equi-dimensional subspaces have maximum robustness (in the MSE sense) with respect to erasures of one subspace among all tight fusion frames, and that the optimal subspace dimension depends on signal-to-noise ratio (SNR). We also prove that tight fusion frames consisting of equi-dimensional subspaces with equal pairwise chordal distances are most robust with respect to two and more subspace erasures, among the class of equi-dimensional tight fusion frames. We call such fusion frames equi-distance tight fusion frames. We prove that the squared chordal distance between the subspaces in such fusion frames meets the so-called simplex bound, and thereby establish connections between equi-distance tight fusion frames and optimal Grassmannian packings. Finally, we present several examples for the construction of equi-distance tight fusion frames.