Foldamers of β-peptides : conformational preference of peptides formed by rigid building blocks : The first MI-IR spectra of a triamide nanosystem

To determine local chirality driven conformational preferences of small aminocyclobutane-1-carboxylic acid derivatives, X-(ACBA) n -Y, their matrix-isolation IR spectra were recorded and analyzed. For the very first time model systems of this kind were deposited in a frozen (~10 K) noble gas matrix to reduce line width and thus, the recorded sharp vibrational lines were analyzed in details. For cis-(S,R)-1 monomer two “zigzag” conformers composed of either a six or an eight-membered H-bonded pseudo ring was identified. For trans-(S,S)-2 stereoisomer a zigzag of an eight-membered pseudo ring and a helical building unit were determined. Both findings are fully consistent with our computational results, even though the relative conformational ratios were found to vary with respect to measurements. For the dimers (S,R,S,S)-3 and (S,S,S,R)-4 as many as four different cis,trans and three different trans,cis conformers were localized in their matrix-isolation IR (MI-IR) spectra. These foldamers not only agree with the previous computational and NMR results, but also unambiguously show for the first time the presence of a structure made of a cis,trans conformer which links a “zigzag” and a helical foldamer via a bifurcated H-bond. The present work underlines the importance of MI-IR spectroscopy, applied for the first time for triamides to analyze the conformational pool of small biomolecules. We have shown that the local chirality of a β-amino acid can fully control its backbone folding preferences. Unlike proteogenic α-peptides, β- and especially (ACBA) n type oligopeptides could thus be used to rationally design and influence foldamer’s structural preferences

30 years of collaboration

We highlight some of the most important cornerstones of the long standing and very fruitful collaboration of the Austrian Diophantine Number Theory research group and the Number Theory and Cryptography School of Debrecen. However, we do not plan to be complete in any sense but give some interesting data and selected results that we find particularly nice. At the end we focus on two topics in more details, namely a problem that origins from a conjecture of Rényi and Erdős (on the number of terms of the square of a polynomial) and another one that origins from a question of Zelinsky (on the unit sum number problem). This paper evolved from a plenary invited talk that the authors gaveat the Joint Austrian-Hungarian Mathematical Conference 2015, August 25-27, 2015 in Győr (Hungary)

Molecular engineering to tune functionality: the case of Cl substituted [Fe(terpy)2]2+

The properties of transition metal complexes and their chemical dynamics can be effectively modified with ligand substitutions, and theory can be a great aid to such molecular engineering. In this paper we first theoretically explore how substitution with a Cl atom at different positions of the terpyridine ligand affects the electronic structure of the [Fe(terpy)2]2+ complex. We found that besides the substitution at position 4’, the next most promising candidate to cause substantial electronic effects is that where the side pyridine ring is substituted at position 5 (beta). Therefore, next we examine in detail the Fe(II) complexes of the 5- chloro and 5,5”-di-chloro derivatives of terpy, theoretically and experimentally, to reveal how these substitutions modify the ground state properties and the lifetime of the excited quintet state in such complexes. In addition, we extend the investigation to the complexes of the analogously substituted derivatives of 4’-SMe-terpy. The substitution at position(s) 5 (and 5”) with Cl lowers the energy of the quintet state and increases its lifetime; the results on the 4’-SMe substituted complexes show similar changes with these two substitutions, verifying that these effects are more or less additive. This study contributes to the enhancement of our molecular engineering toolset for modifying the potential energy landscape of similar complexes

Fuzzy communities and the concept of bridgeness in complex networks

We consider the problem of fuzzy community detection in networks, which complements and expands the concept of overlapping community structure. Our approach allows each vertex of the graph to belong to multiple communities at the same time, determined by exact numerical membership degrees, even in the presence of uncertainty in the data being analyzed. We created an algorithm for determining the optimal membership degrees with respect to a given goal function. Based on the membership degrees, we introduce a new measure that is able to identify outlier vertices that do not belong to any of the communities, bridge vertices that belong significantly to more than one single community, and regular vertices that fundamentally restrict their interactions within their own community, while also being able to quantify the centrality of a vertex with respect to its dominant community. The method can also be used for prediction in case of uncertainty in the dataset analyzed. The number of communities can be given in advance, or determined by the algorithm itself using a fuzzified variant of the modularity function. The technique is able to discover the fuzzy community structure of different real world networks including, but not limited to social networks, scientific collaboration networks and cortical networks with high confidence.Comment: 13 pages, 9 figures. Quality of Fig. 4 reduced due to file size consideration