New inequalities for a triaugle and an internal point

Summary In this note is obtained by a simple geometrical transformation a family of inequalities which connect the distances of an internal point from the vertices of a triangle with its distances from the sides. Stronger forms of old inequalities are also found. To Enrico Bompiani on his scientific Jubiles     

Conformational changes in salivary proline-rich protein 1 upon adsorption to calcium phosphate crystals

Conformational analyses of PRP1, a proline-rich acidic salivary protein and major component of the acquired enamel pellicle, have been carried out in solution and upon binding to two enamel prototypes, hydroxyapatite (HA) and carbonated hydroxyapatite (CHA), using Fourier transform infrared spectroscopy (FTIR) in attenuated total reflection (ATR) mode. We have shown for the first time that, in solution, large portions of PRP1 adopt the hydrated polyproline type II (PPII) helical structure in addition to the random coil structure, with the maximum absorbance of the amide I band around 1620 cm(-1). Upon binding to HA or CHA, the protein undergoes significant conformational changes, loosing a considerable portion of hydrated PPII and random coil domains with a shift in the maximum absorbance to 1666 cm(-1), indicating that a large fraction of the protein is composed of beta turns. A small fraction of PPII in a calcium-bound or anhydrous form (approximately 1642 cm(-1)) was also observed in the HA- and CHA-bound proteins, which could play a role in protein-mineral interactions. The conformational changes in PRP1 adsorbed on CHA and HA were similar in nature; however, these changes were greater in the protein bound to HA. Interestingly, these results are in agreement with protein adsorption data that show that less protein is adsorbed onto CHA than onto HA. Our results demonstrate that binding to apatitic mineral surfaces leads to major conformational changes in PRP1, which might reflect the expulsion of water and the formation of protein-mineral and/or protein-protein interactions in the adsorbed layer.     

High‐resolution high‐performance liquid chromatography with electrospray ionization mass spectrometry and tandem mass spectrometry characterization of a new isoform of human salivary acidic proline‐rich proteins named Roma‐Boston Ser22(Phos) → Phe variant

During a survey of human saliva by a top‐down reversed‐phase high‐performance liquid chromatography with electrospray ionization mass spectrometry approach, two proteins eluting at 27.4 and 28.4 min, with average masses of 15 494 ± 1 and 11 142 ± 1 Da, were detected in a subject from Boston. The Δmass value (4352 Da) of the two proteins was similar to the difference in mass values between intact (150 amino acids, [a.a.]) and truncated acidic proline‐rich proteins (aPRPs; 106 a.a.) suggesting an a.a. substitution in the first 106 residues resulting in a strong reduction in polarity, since under the same experimental conditions aPRPs eluted at ～22.5 min (intact) and 23.5 min (truncated forms). Manual inspection of the high‐resolution high‐performance liquid chromatography with electrospray ionization tandem mass spectra of the truncated isoform showed the replacement of the phosphorylated Ser‐22 in PRP‐3 with a Phe residue. Inspection of the tandem mass spectra of the intact isoform confirmed the substitution, which is allowed by the code transition TCT→TTT and is in agreement with the dramatic increase in elution time. The isoform was also detected in two other subjects, one from Boston (unrelated to the previous) and one from Rome. For this reason we propose to name this variant PRP‐1 (PRP‐3) RB (Roma‐Boston) Ser₂₂(phos)→Phe.     

Fullerene derived molecularly imprinted polymer for chemosensing of adenosine-5′-triphosphate (ATP)

For molecular imprinting of oxidatively electroactive analytes by electropolymerization, we used herein reductively electroactive functional monomers. As a proof of concept, we applied C₆₀ fullerene adducts as such for the first time. For that, we derivatized C₆₀ to bear either an uracil or an amide, or a carboxy addend for recognition of the adenosine-5′-triphosphate (ATP) oxidizable analyte with the ATP-templated molecularly imprinted polymer (MIP-ATP). Accordingly, the ATP complex with all of the functional monomers formed in solution was potentiodynamically electropolymerized to deposit an MIP-ATP film either on an Au electrode of the quartz crystal resonator or on a Pt disk electrode for the piezoelectric microgravimetry (PM) or capacitive impedimetry (CI) determination of ATP, respectively, under the flow-injection analysis (FIA) conditions. The apparent imprinting factor for ATP was ∼4.0. After extraction of the ATP template, analytical performance of the resulting chemosensors, including detectability, sensitivity, and selectivity, was characterized. The limit of detection was 0.3 and 0.03 mM ATP for the PM and CI chemosensor, respectively. The MIP-ATP film discriminated structural analogues of ATP quite well. The Langmuir, Freundlich, and Langmuir–Freundlich isotherms were fitted to the experimental data of the ATP sorption and sorption stability constants appeared to be nearly independent of the adopted sorption model.