Sequential hydration of small protonated peptides

The sequential addition of water molecules to a series of small protonated peptides was studied by equilibrium experiments using electrospray ionization combined with drift cell techniques. The experimental data were compared to theoretical structures of selected hydrated species obtained by molecular mechanics simulations. The sequential water binding energies were measured to be of the order of 7-15 kcal/mol, with the largest values for the first water molecule adding to either a small nonarginine containing peptide (e.g., protonated dialanine) or to a larger peptide in a high charge state (e.g., triply protonated neurotensin). General trends are (a) that the first water molecules are more strongly bound than the following water molecules, (b) that very small peptides (2-3 residues) bind the first few water molecules more strongly than larger peptides, (c) that the first few water molecules bind more strongly to higher charge states than to lower charge states, and (d) that water binds less strongly to a protonated guanidino group (arginine containing peptides) than to a protonated amino group. Experimental differential entropies of hydration were found to be of the order of -20 cal/mol/K although values vary from system to system. At constant experimental conditions the number of water molecules adding to any peptide ion is strongly dependent on the peptide charge state (with higher charge states adding proportionally more water molecules) and only weakly dependent on the choice of peptide. For small peptides molecular mechanics calculations indicate that the first few water molecules add preferentially to the site of protonation until a complete solvation shell is formed around the charge. Subsequent water molecules add either to water molecules of the first solvation shell or add to charge remote functional groups of the peptide. In larger peptides, charge remote sites generally compete more effectively with charge proximate sites even for the first few water molecules.     

HARVESTING ECONOMIC MODELS AND CATCH‐TO‐BIOMASS DEPENDENCE: THE CASE OF SMALL PELAGIC FISH

Abstract In the case of small pelagic fish, it seems reasonable to consider harvest functions depending nonlinearly on fishing effort and fish stock. Indeed, empirical evidence about these fish species suggests that marginal catch does not necessarily react in a linear way neither to changes in fishing effort nor in fish stock levels. This is in contradiction with traditional fishery economic models where catch‐to‐input marginal productivities are normally assumed to be constant. While allowing for nonlinearities in both catch‐to‐effort and catch‐to‐stock parameters, this paper extends the traditional single‐stock harvesting economic model by focusing on the dependence of the stationary solutions upon the nonlinear catch‐to‐stock parameter. Thus, we analyze equilibrium responses to changes in this parameter, which in turn may be triggered either by climatic or technological change. Given the focus in this study on the case of small pelagic fish, the analysis considers positive but small values for the catch‐to‐stock parameter.