Collisional cooling enhances the ability to observe non-covalent interactions within the inducible nitric oxide synthase oxygenase domain: Dimerization,complexation, and dissociation

The investigation of protein quaternary structure, protein-cofactor, and protein-ligand interactions by mass spectrometry is often limited by the fragility of such interactions under experimental conditions. To develop more gentle conditions of perhaps general use, we used as a model for study the oxygenase domain of murine inducible nitric oxide synthase (iNOS), which is homodimeric, binds heme and tetrahydrobiopterin H(4)B cofactors, and the substrate L-arginine. The energetics of the collisions in q2 and in the lens region of the mass spectrometer were manipulated for varying the degree of solvation around the non-covalently bound ions. Furthermore, the number of low-energy collisions in the collision cell of the instrument was varied, focusing and dampening the ion beam. Under gentle source collision conditions, and using multiple low-energy collisions in the collision cell of the mass spectrometer, dimers of the iNOS oxygenase domain containing heme, H(4)B, and arginine were observed intact after electrospraying at pH values near neutrality; a mutant of this protein (Trp188 --> Phe) was monomeric and did not bind cofactors. The pH dependence of the iNOS oxygenase domain under acidic conditions was also studied; while heme remained bound to the protein between pH 2.5 and 4.0, the dimeric structure was disrupted. Our findings confirm that non-covalently bound macromolecular complexes are retained and observable using electrospray mass spectrometry under the appropriate experimental conditions.     

An ab initio molecular orbital study of the grignard reagents CH3MgCl and [CH3MgCl]2: The Schlenk equilibrium

Ab initio molecular orbital calculations are used to study the modified Schlenk equilibrium: 2RMgCl (RMgCl)² MgR₂ + MgCl₂ Mg(Cl₂)MgR₂ with R=H and CH₃. In the absence of any solvents, calculations indicate that the formation of the various possible bridged dimers (RMgCl)₂ is substantially exothermic. However, using dimethylether as a model solvent, we show that the formation of the dimer (Me₂O)(CH₃)Mg(Cl₂)Mg(CH₃)(OMe₂) is exothermic only when entropic effects are included.     

Nonnegative Radix Representations for the Orthant

Let be a nonnegative real matrix which is expanding, i.e. with all eigenvalues , and suppose that is an integer. Let consist of exactly nonnegative vectors in . We classify all pairs such that every in the orthant has at least one radix expansion in base using digits in . The matrix must be a diagonal matrix times a permutation matrix. In addition must be similar to an integer matrix, but need not be an integer matrix. In all cases the digit set can be diagonally scaled to lie in . The proofs generalize a method of Odlyzko, previously used to classify the one--dimensional case.

     

Results and estimates on pseudopowers

Let be a positive integer. We say looks like a power of 2 modulo a prime if there exists an integer such that . First, we provide a simple proof of the fact that a positive integer which looks like a power of modulo all but finitely many primes is in fact a power of . Next, we define an -pseudopower of the base to be a positive integer that is not a power of , but looks like a power of modulo all primes . Let denote the least such . We give an unconditional upper bound on , a conditional result (on ERH) that gives a lower bound, and a heuristic argument suggesting that is about for a certain constant . We compare our heuristic model with numerical data obtained by a sieve. Some results for bases other than are also given.

     

Measurement: It ain't over till it's over

Elby (1993) has raised certain problems that appear to be devastating for modal interpretations of quantum mechanics, but do not arise for Bohm's pilot wave theory. Here I show that the features Elby identifies as objectionable in my version of the modal interpretation have their counterpart in Bohm's theory. To the extent that Bohm's theory works as a no collapse solution to the measurement problem - and I think it does - so does my modal interpretation.