Ernest Julius Wilczynski (in Memoriam)

Ringrazio il collega dell'Università di Chicago di avermi permesso di pubblicare qui un breve sunto della commemorazione da lui scritta; e sono dolente che lo spazio concessomi non me ne abbia permesso la pubblicazione integrale.Guido Fubini     

Simple pictorial mathematics problems for children: locating sources of cognitive load and how to reduce it

ZDM – Mathematics Education - Pictorial representations are often used to help children understand the situation described in a given number-sentence scheme. These static pictorial problems...     

A wider convergence area for the MSTMAOR iteration methods for LCP

In this paper, based on the Hermitian and skew-Hermitian splitting, we give a generalized modified Hermitian and skew-Hermitian splitting (GMHSS) method to solve singular complex symmetric linear systems, this method has two parameters. We give the semi-convergent conditions, and some numerical experiments are given to illustrate the efficiency of this method.     

On the 4-dissections of certain infinite products

In this note, we give a generalization of Hirschhorn’s formulas on the 4-dissections of Ramanujan’s continued fraction R(q) and R ^?1(q) which were conjectured by Hirschhorn and proved by Lewis and Liu.     

A configuration interaction study of the spin dipole-dipole parameters for formaldehyde and methylene

The electron spin dipole-dipole contribution to the zero field splitting has been evaluated for the ³A₂ (n → π*) and ³A₁ (π → π*) states of formaldehyde using a CI wave function constructed from contracted Gaussian-lobe functions. The values D = 0.539 cm^?1 and E = 0.031 cm^?1 were obtained for the ³A₂(n → π*) state and D = ?0.588 cm^?1 and E = 0.058 cm^?1 were obtained for the ³A₁ (π → π*) state using the CI wave function constructed from SCF orbitals of the respective parent configurations. An analysis of the effect of CI on the parameters is given for the ³A₂ (n n → π*) state of formaldehyde and the ³B₁ ground state of methylene. Numerical results are given which show that internally consistent self-consistent field orbitals (ICSCF ) are superior to canonical SCF orbitals as a starting point for a CI calculation. Our CI wave function for the ¹A₁ ground state gave an energy of ?114.13658 hartrees which is significantly lower than any previously reported energy calculation. This wave function gives a dipole moment of 2.22 Debye (C⁺O^?) in good agreement with the experimental value of 2.33 ± 0.02 Debye.     

Rotation and inversion barriers in 2-lithio-2-phenyl-1,3-dithianes

The barriers to phenyl rotation in 2-lithio-2-phenyl-cis-4,6-dimethyl-, 2-lithio-2-phenyl-4,4,6-trimethyl- and 2-lithio-2-phenyl-trans-4,6-dimethyl-1,3-dithiane are compared in tetrahydrofuran (THF) and hexamethylphosphortriamide (HMPA). In the first two cases, the barriers in THF are lower than those in HMPA, presumably because the lithio compound exists as a tight ion pair in THF but as a solvent-separated ion pair (with more delocalization of charge into the phenyl ring) in HMPA. However, in the trans-4,6-dimethyl compound the barriers are the same in the two solvents and nearly equal to the barriers for ring reversal. It is concluded that in this compound the rate-determining step for phenyl rotation may actually be ring reversal, at least in solvent HMPA.     

Conformational analysis of trans-2,3-diaryloxy-1,4-dioxanes. A tool for discriminating between steric and electronic effects in the position of

The conformation of several $\text{trans}$-2,3-diaryloxy-1,4-dioxanes has been studied using ¹H NMR techniques. $\text{Trans}$-2,3-bis(4-nitrophenoxy)-1,4-dioxane and $\text{trans}$-2,3-bis(4-methoxyphenoxy)-1,4-dioxane have been found to be predominantly ( ≈98%) in diaxial conformation in CDCl₃). On the other hand, $\text{trans}$-2,3-bis(2,6-dimethylphenoxy)-1,4-dioxane exists in the same conditions as a 66:33 mixture of diaxial and diequatorial conformers. An explanation based on the fulfilment of the exo-anomeric effect is provided.     

Large concentration effects on conformational equilibria

The conformational equilibrium in $\text{cis}$-3-Hydroxythiane S-oxide (Scheme 1) is strongly concentration dependent, being affected by intermolecular hydrogen bonding at high concentration.     

Target-templated de novo design of macrocyclic d-/l-peptides: discovery of drug-like inhibitors of PD-1

Peptides are a rapidly growing class of therapeutics with various advantages over traditional small molecules, especially for targeting difficult protein–protein interactions. However, current structure-based methods are largely limited to natural peptides and are not suitable for designing bioactive cyclic topologies that go beyond natural l-amino acids. Here, we report a generalizable framework that exploits the computational power of Rosetta, in terms of large-scale backbone sampling, side-chain composition and energy scoring, to design heterochiral cyclic peptides that bind to a protein surface of interest. To showcase the applicability of our approach, we developed two new inhibitors (PD-i3 and PD-i6) of programmed cell death 1 (PD-1), a key immune checkpoint in oncology. A comprehensive biophysical evaluation was performed to assess their binding to PD-1 as well as their blocking effect on the endogenous PD-1/PD-L1 interaction. Finally, NMR elucidation of their in-solution structures confirmed our de novo design approach.

In silico design of heterochiral cyclic peptides that bind to a specific surface patch on the target protein (PD-1, in this case) and disrupt protein–protein interactions.