An extremal problem related to probability

Summary We consider a walk from a stateA ₁ to a stateA _n+1 in which the probability of remaining atA _i isp _i , and the probability of progressing fromA _i toA _i+1 is 1 –p _i . The probabilityW _nk of reachingA _n+1 fromA ₁ in exactlyn + k steps can then be expressed as a polynomial of degreen + k in then variablesp ₁,,p _n . We determine the maximum value ofW _nk and the (unique) choice (p ₁,,p _n ) for which this extremum occurs.Dedicated to Professor Otto Haupt with best wishes on his 100th birthday     

The measure of non-normal sets

Summary It is well-known that almost every number in [0, 1] is normal in base 2, in the sense of Lebesgue measure. Kahane and Salem asked whether the same is true with respect to any Borel measure whose Fourier-Stieltjes coefficients vanish at infinity — in other words, whether the set of non-normal numbers is a set of uniqueness in the wide sense. We show that this is not the case. In fact, we give best-possible conditions on the rate of decay of in order that -almost every number be normal. The techniques include, on the one hand, probability measures with respect to which the binary digits in [0, 1] are independent only by blocks, rather than individually, and on the other hand, the strong law of large numbers for weakly correlated random variables.This work was partially supported by an NSF Graduate Fellowship, NSF Grant MCS-82-01602, and an AMS Research Fellowship.     

A Mets motif peptide found in copper transport proteins selectively binds Cu(I) with methionine-only coordination

Mets motifs, which refer to methionine-rich sequences found in the high-affinity copper transporter Ctr1, also appear in other proteins involved in copper trafficking and homeostasis, including other Ctrs as well as Pco and Cop proteins isolated from copper-resistant bacteria. To understand the coordination chemistry utilized by these proteins, we studied the copper binding properties of a peptide labeled Mets7-PcoC with the sequence Met-Thr-Gly-Met-Lys-Gly-Met-Ser. By comparing this sequence to a series of mutants containing noncoordinating norleucine in place of methionine, we confirm that all three methionine residues are involved in a thioether-only binding site that is selective for Cu(I). Two independent methods, one based on mass spectrometry and one based on rate differences for the copper-catalyzed oxidation of ascorbic acid, provide an effective K(D) of approximately 2.5 microM at pH 4.5 for the 1:1 complex of Mets7-PcoC with Cu(I). These results establish that a relatively simple peptide containing an MX(2)MX(2)M motif is sufficient to bind Cu(I) with an affinity that corresponds well with its proposed biological function of extracellular copper acquisition.     

Characterization of N-terminal processing of group VIA phospholipase A<Subscript>2</Subscript> and of potential cleavage sites of amyloid precursor protein constructs by automated identification of signature peptides in LC/MS/MS analyses of proteolytic digests

Dysregulation of proteolytic processing of the amyloid precursor protein (APP) contributes to the pathogenesis of Alzheimer's Disease, and the Group VIA phospholipase A(2) (iPLA(2)beta) is the dominant PLA(2) enzyme in the central nervous system and is subject to regulatory proteolytic processing. We have identified novel N-terminal variants of iPLA(2)beta and previously unrecognized proteolysis sites in APP constructs with a C-terminal 6-myc tag by automated identification of signature peptides in LC/MS/MS analyses of proteolytic digests. We have developed a Signature-Discovery (SD) program to characterize protein isoforms by identifying signature peptides that arise from proteolytic processing in vivo. This program analyzes MS/MS data from LC analyses of proteolytic digests of protein mixtures that can include incompletely resolved components in biological samples. This reduces requirements for purification and thereby minimizes artifactual modifications during sample processing. A new algorithm to generate the theoretical signature peptide set and to calculate similarity scores between predicted and observed mass spectra has been tested and optimized with model proteins. The program has been applied to the identification of variants of proteins of biological interest, including APP cleavage products and iPLA(2)beta, and such applications demonstrate the utility of this approach.     

Calorimeters for biotechnology

The isothermal and temperature scanning calorimeters manufactured by Calorimetry Sciences Corporation are briefly described. Applications of calorimetry to determine thermodynamics and kinetics of reactions of interest in biotechnology are described with illustrative examples.     

Identification of a highly effective asymmetric phase-transfer catalyst derived from α-methylnaphthylamine

A library of quaternary ammonium salts has been generated via reaction of simple chiral amines with a series of conformationally dynamic biphenyl units. Screening of this library against the alkylation of a glycine imine has led to the identification of a highly effective asymmetric phase-transfer catalyst derived from α-methylnaphthylamine.     

Interfacial electrical properties of DNA-modified diamond thin films: intrinsic response and hybridization-induced field effects

We have investigated the frequency-dependent interfacial electrical properties of nanocrystalline diamond films that were covalently linked to DNA oligonucleotides and how these properties are changed upon exposure to complementary and noncomplementary DNA oligonucleotides. Frequency-dependent electrical measurements at the open-circuit potential show significant changes in impedance at frequencies of >10(4) Hz when DNA-modified diamond films are exposed to complementary DNA, with only minimal changes when exposed to noncomplementary DNA molecules. Measurements as a function of potential show that at 10(5) Hz, the impedance is dominated by the space-charge region of the diamond film. DNA molecules hybridizing at the interface induce a field effect in the diamond space-charge layer, altering the impedance of the diamond film. By identifying a range of impedances where the impedance is dominated by the diamond space-charge layer, we show that it possible to directly observe DNA hybridization, in real time and without additional labels, via simple measurement of the interfacial impedance.     

Adhesive transfer of thin viscoelastic films

Micellar suspensions of acrylic diblock copolymers are excellent model materials for studying the adhesive transfer of viscoelastic solids. The micellar structure is maintained in films with a variety of thicknesses, giving films with a well-defined structure and viscoelastic character. Thin films were cast onto elastomeric silicone substrates from micellar suspensions in butanol, and the adhesive interactions between these coated elastomeric substrates and a rigid indenter were quantified. By controlling the adhesive properties of the film/indenter and film/substrate interfaces we were able to obtain very clean transfer of the film from the substrate to the portion of the glass indenter with which the film was in contact. Adhesive failure at the film/substrate interface occurs when the film/indenter interface is able to support an applied energy release rate that is sufficient to result in cavity nucleation at the film/substrate interface. Cavity formation is rapidly followed by delamination of the entire region under the indenter. The final stage in the transfer process involves the failure of the film that bridges the indenter and the elastomeric substrate. This film is remarkably robust and is extended to three times its original width prior to failure. Failure of this film occurs at the periphery of the indenter, giving a transferred film that conforms to the original contact area between the indenter and the coated substrate.