The hard-soft acid-base principle in enzymatic catalysis: dual reactivity of phosphoenolpyruvate.

In this paper, the chemical reactivity of C3 of phosphoenolpyruvate (PEP) has been analyzed in terms of density functional theory quantified through quantum chemistry calculations. PEP is involved in a number of important enzymatic reactions, in which its C3 atom behaves like a base. In three different enzymatic reactions analyzed here, C3 sometimes behaves like a soft base and sometimes behaves like a hard base in terms of the hard-soft acid-base principle. This dual nature of C3 of PEP was found to be related to the conformational change of the molecule. This leads to a testable hypothesis: that PEP adopts particular conformations in the enzyme-substrate complexes of different PEP-using enzymes, and that the enzymes control the reactivity through controlling the dihedral angle between the carboxylate and the C==C double bond of PEP.

The resource consumption principle: attention and memory in volumes of neural tissue.

In the cerebral cortex, the small volume of the extracellular space in relation to the volume enclosed by synapses suggests an important functional role for this relationship. It is well known that there are atoms and molecules in the extracellular space that are absolutely necessary for synapses to function (e.g., calcium). I propose here the hypothesis that the rapid shift of these atoms and molecules from extracellular to intrasynaptic compartments represents the consumption of a shared, limited resource available to local volumes of neural tissue. Such consumption results in a dramatic competition among synapses for resources necessary for their function. In this paper, I explore a theory in which this resource consumption plays a critical role in the way local volumes of neural tissue operate. On short time scales, this principle of resource consumption permits a tissue volume to choose those synapses that function in a particular context and thereby helps to integrate the many neural signals that impinge on a tissue volume at any given moment. On longer time scales, the same principle aids in the stable storage and recall of information. The theory provides one framework for understanding how cerebral cortical tissue volumes integrate, attend to, store, and recall information. In this account, the capacity of neural tissue to attend to stimuli is intimately tied to the way tissue volumes are organized at fine spatial scales.

Groups, information theory, and Einstein's likelihood principle

We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to the composition of independent systems, in the context of a recently proposed generalization of the Shannon-Khinchin axioms. We associate to each member of a large class of entropies a generalized information measure, satisfying the additivity property on a set of independent systems as a consequence of the underlying group law. At the same time, we also show that Einstein's likelihood function naturally emerges as a byproduct of our informational interpretation of (generally nonadditive) entropies. These results confirm the adequacy of composable entropies both in physical and social science contexts.