Resin-bound sulfonyl azides: efficient loading and activation strategy for the preparation of the N-acyl sulfonamide linker

This paper describes an optimized protocol for the efficient loading of resin-bound aminoethane sulfonyl azides by either Boc- or Fmoc-protected amino thioacids. The resulting N-acyl sulfonamide is a convenient linker for use in Boc- or Fmoc-based solid-phase peptide synthesis. Activation of the N-acyl sulfonamide via a microwave-assisted alkylation procedure and subsequent treatment with functionalized nucleophiles yields C-terminally modified peptides that can be applied in chemoselective (bio)conjugation or ligation reactions.     

Dynamic effects on j-couplings across hydrogen bonds in proteins

We combine molecular dynamics simulation (MD) with density functional theory (DFT)/finite perturbation theory (FPT) to obtain the Fermi contact contributions to the 3hJNC' couplings in the SMN Tudor domain. Our results show that the effect of conformational motion needs to be considered for the accurate prediction of these scalar couplings. For hydrogen bonds in the beta-sheet regions, the calculated cumulative J-coupling averages remain constant after the first 200 ps. In the more flexible regions at the edges of the beta-sheets, the cumulative J-coupling averages vary over the 500-ps trajectory, providing a qualitative insight into the degree of conformational motion in different regions of the protein.     

Transient-time correlation function applied to mixed shear and elongational flows

The transient-time correlation function (TTCF) method is used to calculate the nonlinear response of a homogeneous atomic fluid close to equilibrium. The TTCF response of the pressure tensor subjected to a time-independent planar mixed flow of shear and elongation is compared to directly averaged non-equilibrium molecular dynamics (NEMD) simulations. We discuss the consequence of noise in simulations with a small rate of deformation. The generalized viscosity for planar mixed flow is also calculated with TTCF. We find that for small rates of deformation, TTCF is far more efficient than direct averages of NEMD simulations. Therefore, TTCF can be applied to fluids with deformation rates which are much smaller than those commonly used in NEMD simulations. Ultimately, TTCF applied to molecular systems is amenable to direct comparison between NEMD simulations and experiments and so in principle can be used to study the rheology of polymer melts in industrial processes.     

Automated Solid‐Phase Synthesis and Structural Investigation of β‐Peptidosulfonamides and β‐Peptidosulfonamide/β‐Peptide Hybrids: β‐Peptidosulfonamide and β‐Peptide Foldamers are Two of a Different Kind

Fmoc‐protected β‐aminoethane sulfonylchlorides can be employed for efficient automated solid phase synthesis of β‐peptidosulfonamides and β‐peptidosulfonamide/β‐peptide hybrids containing one or more β‐peptidosulfonamide residues. Thus, Fmoc‐protected β‐aminoethane sulfonylchlorides 5a – c led to the hexa‐β‐peptidosulfonamide 9 and the nona‐β‐peptidosulfonamide 10 . In addition, the β‐peptidosulfonamide/β‐peptide hybrids 13 and 16 , consisting of six and nine β‐residues, respectively, and containing a single β‐peptidosulfonamide unit in the middle, as well as the peptidosulfonamide/β‐peptide hybrid 15 with nine β‐residues, including an N‐terminal β‐peptidosulfonamide residue, were synthesized by automated solid‐phase synthesis. Both CD and NMR spectroscopic measurements did not indicate any helical secondary structure for 9 and 10 . As was shown by CD‐measurements, the β‐peptidosulfonamide residue in the hybrids 13, 15 , and 16 acts as a ‘helix breaker', especially when located in the middle of the hybrid chain ( 13 and 16 ), but, although to a lesser extent, also at the N‐terminus.     

The diatropic sigma ring currents of [pi2s + pi2s + pi2s] pericyclic transition states

Ab initio current-density maps for the (4n + 2)-electron transition states of two thermally allowed [pi2s + pi2s + pi2s] trimerisations, of ethyne to benzene (1), and of ethene to cyclohexane (2), show that both support sigma diatropic ring currents, dominated by four-electron sigma --> sigma* virtual excitation of HOMO electrons.     

Random graph asymptotics on high-dimensional tori II: volume, diameter and mixing time

For critical bond-percolation on high-dimensional torus, this paper proves sharp lower bounds on the size of the largest cluster, removing a logarithmic correction in the lower bound in Heydenreich and van der Hofstad (Comm Math Phys 270(2):335?C358, 2007). This improvement finally settles a conjecture by Aizenman (Nuclear Phys B 485(3):551?C582, 1997) about the role of boundary conditions in critical high-dimensional percolation, and it is a key step in deriving further properties of critical percolation on the torus. Indeed, a criterion of Nachmias and Peres (Ann Probab 36(4):1267?C1286, 2008) implies appropriate bounds on diameter and mixing time of the largest clusters. We further prove that the volume bounds apply also to any finite number of the largest clusters. Finally, we show that any weak limit of the largest connected component is non-degenerate, which can be viewed as a significant sign of critical behavior. The main conclusion of the paper is that the behavior of critical percolation on the high-dimensional torus is the same as for critical Erd?s-Rényi random graphs.     

Organic modification and subsequent biofunctionalization of porous anodic alumina using terminal alkynes

Porous anodic alumina (PAA) is a well-defined material that has found many applications. The range of applications toward sensing and recognition can be greatly expanded if the alumina surface is covalently modified with an organic monolayer. Here, we present a new method for the organic modification of PAA based on the reaction of terminal alkynes with the alumina surface. The reaction results in the the formation of a monolayer within several hours at 80 °C and is dependent on both oxygen and light. Characterization with X-ray photoelectron spectroscopy and infrared spectroscopy indicates formation of a well-defined monolayer in which the adsorbed species is an oxidation product of the 1-alkyne, namely, its α-hydroxy carboxylate. The obtained monolayers are fairly stable in water and at elevated temperatures, as was shown by monitoring the water contact angle. Modification with 1,15-hexadecadiyne resulted in a surface that has alkyne end groups available for further reaction, as was demonstrated by the subsequent reaction of N-(11-azido-3,6,9-trioxaundecyl)trifluoroacetamide with the modified surface. Biofunctionalization was explored by coupling 11-azidoundecyl lactoside to the surface and studying the subsequent adsorption of the lectin peanut agglutinin (PNA) and the yeast Candida albicans, respectively. Selective and reversible binding of PNA to the lactosylated surfaces was demonstrated. Moreover, PNA adsorption was higher on surfaces that exposed the β-lactoside than on those that displayed the α anomer, which was attributed to surface-associated steric hindrance. Likewise, the lactosylated surfaces showed increased colonization of C. albicans compared to unmodified surfaces, presumably due to interactions involving the cell wall β-glucan. Thus, this study provides a new modification method for PAA surfaces and shows that it can be used to induce selective adsorption of proteins and microorganisms.     

Aromaticity of planar Si6 rings in silicon–lithium clusters

Ipsocentric calculations of current density at the B3LYP/6-311++G(2d,2p) level show that the planar Si₆ ring supports a diatropic π ring current of about half the strength of the equivalent π current in benzene, both in the presumed global optimum geometry of Si₆Li₆ and in geometries occupying higher-energy local minima, corroborating the attribution of aromaticity to this silicon analogue of benzene.     

Critical behavior in inhomogeneous random graphs

We study the critical behavior of inhomogeneous random graphs in the so‐called rank‐1 case, where edges are present independently but with unequal edge occupation probabilities. The edge occupation probabilities are moderated by vertex weights, and are such that the degree of vertex i is close in distribution to a Poisson random variable with parameter w_i, where w_i denotes the weight of vertex i. We choose the weights such that the weight of a uniformly chosen vertex converges in distribution to a limiting random variable W. In this case, the proportion of vertices with degree k is close to the probability that a Poisson random variable with random parameter W takes the value k. We pay special attention to the power‐law case, i.e., the case where \begin{align*}{\mathbb{P}}(W\geq k)\end{align*} is proportional to k^‐(τ‐1) for some power‐law exponent τ > 3, a property which is then inherited by the asymptotic degree distribution. We show that the critical behavior depends sensitively on the properties of the asymptotic degree distribution moderated by the asymptotic weight distribution W. Indeed, when \begin{align*}{\mathbb{P}}(W > k) \leq ck^{-(\tau-1)}\end{align*} for all k ≥ 1 and some τ > 4 and c > 0, the largest critical connected component in a graph of size n is of order n^2/3, as it is for the critical Erd?s‐Rényi random graph. When, instead, \begin{align*}{\mathbb{P}}(W > k)=ck^{-(\tau-1)}(1+o(1))\end{align*} for k large and some τ∈(3,4) and c > 0, the largest critical connected component is of the much smaller order n^{(τ‐2)/(τ‐1)}. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 42, 480–508, 2013     

When is a Scale-Free Graph Ultra-Small?

In this paper we study typical distances in the configuration model, when the degrees have asymptotically infinite variance. We assume that the empirical degree distribution follows a power law with exponent \(\tau \in (2,3)\), up to value \(n^{{\beta _n}}\) for some \({\beta _n}\gg (\log n)^{-\gamma }\) and \(\gamma \in (0,1)\). This assumption is satisfied for power law i.i.d. degrees, and also includes truncated power-law empirical degree distributions where the (possibly exponential) truncation happens at \(n^{{\beta _n}}\). These examples are commonly observed in many real-life networks. We show that the graph distance between two uniformly chosen vertices centers around \(2 \log \log (n^{{\beta _n}}) / |\log (\tau -2)| + 1/({\beta _n}(3-\tau ))\), with tight fluctuations. Thus, the graph is an ultrasmall world whenever \(1/{\beta _n}=o(\log \log n)\). We determine the distribution of the fluctuations around this value, in particular we prove these form a sequence of tight random variables with distributions that show \(\log \log \)-periodicity, and as a result it is non-converging. We describe the topology and number of shortest paths: We show that the number of shortest paths is of order \(n^{f_n{\beta _n}}\), where \(f_n \in (0,1)\) is a random variable that oscillates with n. We decompose shortest paths into three segments, two ‘end-segments’ starting at each of the two uniformly chosen vertices, and a middle segment. The two end-segments of any shortest path have length \(\log \log (n^{{\beta _n}}) / |\log (\tau -2)|\)+tight, and the total degree is increasing towards the middle of the path on these segments. The connecting middle segment has length \(1/({\beta _n}(3-\tau ))\)+tight, and it contains only vertices with degree at least of order \(n^{(1-f_n){\beta _n}}\), thus all the degrees on this segment are comparable to the maximal degree. Our theorems also apply when instead of truncating the degrees, we start with a configuration model and we remove every vertex with degree at least \(n^{{\beta _n}}\), and the edges attached to these vertices. This sheds light on the attack vulnerability of the configuration model with infinite variance degrees.