Theoretical studies on the hydrolysis of mono-phosphate and tri-phosphate in gas phase and aqueous solution

Phosphate hydrolysis by GTPases plays an important role as a molecular switch in signal transduction and as an initiator of many other biological processes. Despite the centrality of this ubiquitous reaction, the mechanism is still poorly understood. As a first step to understand the mechanisms of this process, the nonenzymatic hydrolysis of mono-phosphate and tri-phosphate esters were systematically studied in gas phase and aqueous solution using hybrid density functional methods. The dielectric effect of the environment on the energetics of these processes was also explored. Theoretical results show that for mono-phosphate ester, the dissociative pathway is much more favorable than the associative pathway. However, the reaction barriers for the dissociative and associative pathways of tri-phosphate hydrolysis are very close in aqueous solution, though the dissociative pathway is more favorable in the gas phase. High dielectric solvents, such as water, significantly lower the activation barrier of the associative pathway due to the greater solvation energy of the associative transition states than that of the reactant complex. By contrast, the barrier of the dissociative pathway, with respect to the gas phase, is less sensitive to the surrounding dielectric. In the associative hydrolysis pathway of the tri-phosphate ester, negative charge is transferred from the gamma-phosphate to beta-phosphate through the bridging ester oxygen and results in Pgamma-O bond dissociation. No analogous charge transfer was observed in the dissociative pathway, where Pgamma-O bond dissociation resulted from proton transfer from the gamma-phosphate to the bridge oxygen. Finally, the active participation of local water molecules can significantly lower the activation energy of the dissociative pathway for both mono-phosphate and tri-phosphate.     

Endothermic ion molecule reactions

Endothermic ion-molecule reactions in a tandem mass spectrometer have been used for a number of years for determining thermodynamic quantities, such as heats of formation and proton affinities, for gaseous ions. Recently, the reactive, endothermic collision has been exploited as an analytical technique for the structural analysis of peptides and other biomolecules. The technique is based upon the endothermic transfer of protons associated with amide bonds to ammonia. This reaction proceeds via a long-lived collision complex. When additional beam energy is supplied, other dissociation channels are opened up, leading to the production of sequence ions for the mass-selected, protonated analyte that are normally observed in high energy collision-induced dissociation spectra. The advantage, however, is that such spectra can be produced at very low beam energies. In this article, the rationale for developing this scheme, and its roots in previous ion-molecule studies, are explored.     

α-contractions and attractors for dissipative semilinear hyperbolic equations and systems

Summary In this paper we discuss the existence of compact attractor for the abstract semilinear evolution equation u=Au+f(t, u); the results are applied to damped partial differential equations of hyperbolic type. Our approach is a combination of Liapunov method with the theory of -eontractions.     

Fractal landscapes in biological systems: long-range correlations in DNA and interbeat heart intervals

Here we discuss recent advances in applying ideas of fractals and disordered systems to two topics of biological interest, both topics having common the appearance of scale-free phenomena, i.e., correlations that have no characteristic length scale, typically exhibited by physical systems near a critical point and dynamical systems far from equilibrium. (i) DNA nucleotide sequences have traditionally been analyzed using models which incorporate the possibility of short-range nucleotide correlations. We found, instead, a remarkably long-range power law correlation. We found such long-range correlations in intron-containing genes and in non-transcribed regulatory DNA sequences as well as intragenomic DNA, but not in cDNA sequences or intron-less genes. We also found that the myosin heavy chain family gene evolution increases the fractal complexity of the DNA landscapes, consistent with the intron-late hypothesis of gene evolution. (ii) The healthy heartbeat is traditionally thought to be regulated according to the classical principle of homeostasis, whereby physiologic systems operate to reduce variability and achieve an equilibrium-like state. We found, however, that under normal conditions, beat-to-beat fluctuations in heart rate display long-range power law correlations.     

Sets of vectors with many orthogonal paris:

What is the most number of vectors inR ^d such that anyk+1 contain an orthogonal pair? The 24 positive roots of the root systemF ₄ inR ⁴ show that this number could exceeddk.