We discuss our results in the context of the current debate about criticality in biology. We conclude that the emergent behavior reported probably arises from the necessity to balance two conflicting imperatives: ( i) the exploration of foraging space by individuals and ( ii) the protection from predators offered by being part of large, cohesive groups. In particular, the intensity of sheep allelomimetic behavior plays a key role in the group’s ability to increase the per capita grazing surface while minimizing the time needed to regroup into a tightly packed configuration. This offers, in turn, an insight on the individual stimulus/response functions that can generate such intermittent behavior.
As a proof of principle, we introduce an agent-based model with individual behavioral shifts, which we show to account faithfully for all collective properties observed. Our analysis reveals strongly intermittent collective dynamics consisting of fast, avalanche-like regrouping events distributed on all experimentally accessible scales. We study this phenomenon quantitatively in large groups of grazing Merino sheep under controlled experimental conditions. The results of kinetic experiments confirmed these predictions.Among the many fascinating examples of collective behavior exhibited by animal groups, some species are known to alternate slow group dispersion in space with rapid aggregation phenomena induced by a sudden behavioral shift at the individual level.
Kinetic derivations for the reaction of the enzyme with the conventional substrate gamma-glutamyl-p-nitroanilide predict either linear or nonlinear double-reciprocal plots, depending on the prevalence of the hydrolytic, autotranspeptidation, or transpeptidation reactions. This mechanism predicts the formation of an alpha-methyl-gamma-glutamyl-enzyme intermediate, which can react with an amino acid to form the transpeptidation product or in the absence of, or in the presence of low concentrations of amino acids, can react with water to form the hydrolytic products. A scheme of such a mechanism is presented. Initial velocity measurements in which the concentration of L-alpha-methyl-gamma-glutamyl-L-alpha-aminobutyrate was varied at several fixed acceptor concentrations, and either the release of alpha-aminobutyrate or the formation of the transpeptidation products was determined, yielded results which are consistent with a ping-pong mechanism modified by a hydrolytic shunt. When the enzyme was incubated with conventional substrates, such as glutathione or gamma-glutamyl-p-nitroanilide and an amino acid acceptor, hydrolysis, autotranspeptidation, and transpeptidation to the acceptor occurred concurrently. The presence of the methyl group on the alpha-carbon apparently prevents enzymatic transfer of the L-alpha-methyl-gamma-glutamyl residue to the amino group of the substrate itself (autotranspeptidation). In the absence of acceptor only hydrolysis occurred, and no transpeptidation products were detected. When the substrate was incubated with the enzyme in the presence of an amino acid or peptide acceptor, the corresponding L-alpha-methyl-gamma-glutamyl derivatives of the acceptors were formed. The kinetics of sheep kidney gamma-glutamyl transpeptidase was studied using a novel substrate L-alpha-methyl-gamma-glutamyl-L-alpha-aminobutyrate.
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