Ionophores and receptors using cation-π interactions: Collarenes

Cation-π interactions are important forces in molecular recognition by biological receptors, enzyme catalysis, and crystal engineering. We have harnessed these interactions in designing molecular systems with circular arrangement of benzene units that are capable of acting as ionophores and models for biological receptors. [n]Collarenes are promising candidates with high selectivity for a specific cation, depending on n, because of their structural rigidity and well-defined cavity size. The interaction energies of [n]collarenes with cations have been evaluated by using ab initio calculations. The selectivity of these [n]collarenes in aqueous solution was revealed by using statistical perturbation theory in conjunction with Monte Carlo and molecular dynamics simulations. It has been observed that in [n]collarenes the ratio of the interaction energies of a cation with it and the cation with the basic building unit (benzene) can be correlated to its ion selectivity. We find that collarenes are excellent and efficient ionophores that bind cations through cation-π interactions. [6]Collarene is found to be a selective host for Li+ and Mg2+, [8]collarene for K+ and Sr2+, and [10]collarene for Cs+ and Ba2+. This finding indicates that [10]collarene and [8]collarene could be used for effective separation of highly radioactive isotopes, 137Cs and 90Sr, which are major constituents of nuclear wastes. More interestingly, collarenes of larger cavity size can be useful in capturing organic cations. [12]Collarene exhibits a pronounced affinity for tetramethylammonium cation and acetylcholine, which implies that it could serve as a model for acetylcholinestrase. Thus, collarenes can prove to be novel and effective ionophores/model-receptors capable of heralding a new direction in molecular recognition and host-guest chemistry.

Recruitment and replacement of hippocampal neurons in young and adult chickadees: an addition to the theory of hippocampal learning.

We used [3H]thymidine to document the birth of neurons and their recruitment into the hippocampal complex (HC) of juvenile (4.5 months old) and adult blackcapped chickadees (Parus atricapillus) living in their natural surroundings. Birds received a single dose of [3H]thymidine in August and were recaptured and killed 6 weeks later, in early October. All brains were stained with Cresyl violet, a Nissl stain. The boundaries of the HC were defined by reference to the ventricular wall, the brain surface, or differences in neuronal packing density. The HC of juveniles was as large as or larger than that of adults and packing density of HC neurons was 31% higher in juveniles than in adults. Almost all of the 3H-labeled HC neurons were found in a 350-m-wide layer of tissue adjacent to the lateral ventricle. Within this layer the fraction of 3H-labeled neurons was 50% higher in juveniles than in adults. We conclude that the HC of juvenile chickadees recruits more neurons and has more neurons than that of adults. We speculate that juveniles encounter greater environmental novelty than adults and that the greater number of HC neurons found in juveniles allows them to learn more than adults. At a more general level, we suggest that (i) long-term learning alters HC neurons irreversibly; (ii) sustained hippocampal learning requires the periodic replacement of HC neurons; (iii) memories coded by hippocampal neurons are transferred elsewhere before the neurons are replaced.

An equilibrium statistical model for the spreading phase of open-ocean convection

A “most probable state” equilibrium statistical theory for random distributions of hetons in a closed basin is developed here in the context of two-layer quasigeostrophic models for the spreading phase of open-ocean convection. The theory depends only on bulk conserved quantities such as energy, circulation, and the range of values of potential vorticity in each layer. The simplest theory is formulated for a uniform cooling event over the entire basin that triggers a homogeneous random distribution of convective towers. For a small Rossby deformation radius typical for open-ocean convection sites, the most probable states that arise from this theory strongly resemble the saturated baroclinic states of the spreading phase of convection, with a stabilizing barotropic rim current and localized temperature anomaly.

Forming classes by stimulus frequency: Behavior and theory

Visual classification is the way we relate to different images in our environment as if they were the same, while relating differently to other collections of stimuli (e.g., human vs. animal faces). It is still not clear, however, how the brain forms such classes, especially when introduced with new or changing environments. To isolate a perception-based mechanism underlying class representation, we studied unsupervised classification of an incoming stream of simple images. Classification patterns were clearly affected by stimulus frequency distribution, although subjects were unaware of this distribution. There was a common bias to locate class centers near the most frequent stimuli and their boundaries near the least frequent stimuli. Responses were also faster for more frequent stimuli. Using a minimal, biologically based neural-network model, we demonstrate that a simple, self-organizing representation mechanism based on overlapping tuning curves and slow Hebbian learning suffices to ensure classification. Combined behavioral and theoretical results predict large tuning overlap, implicating posterior infero-temporal cortex as a possible site of classification.

Stochastic game theory: For playing games, not just for doing theory

Recent theoretical advances have dramatically increased the relevance of game theory for predicting human behavior in interactive situations. By relaxing the classical assumptions of perfect rationality and perfect foresight, we obtain much improved explanations of initial decisions, dynamic patterns of learning and adjustment, and equilibrium steady-state distributions.

Advances in random matrix theory, zeta functions, and sphere packing

Over four hundred years ago, Sir Walter Raleigh asked his mathematical assistant to find formulas for the number of cannonballs in regularly stacked piles. These investigations aroused the curiosity of the astronomer Johannes Kepler and led to a problem that has gone centuries without a solution: why is the familiar cannonball stack the most efficient arrangement possible? Here we discuss the solution that Hales found in 1998. Almost every part of the 282-page proof relies on long computer verifications. Random matrix theory was developed by physicists to describe the spectra of complex nuclei. In particular, the statistical fluctuations of the eigenvalues (“the energy levels”) follow certain universal laws based on symmetry types. We describe these and then discuss the remarkable appearance of these laws for zeros of the Riemann zeta function (which is the generating function for prime numbers and is the last special function from the last century that is not understood today.) Explaining this phenomenon is a central problem. These topics are distinct, so we present them separately with their own introductory remarks.

An information theory model of hydrophobic interactions.

A molecular model of poorly understood hydrophobic effects is heuristically developed using the methods of information theory. Because primitive hydrophobic effects can be tied to the probability of observing a molecular-sized cavity in the solvent, the probability distribution of the number of solvent centers in a cavity volume is modeled on the basis of the two moments available from the density and radial distribution of oxygen atoms in liquid water. The modeled distribution then yields the probability that no solvent centers are found in the cavity volume. This model is shown to account quantitatively for the central hydrophobic phenomena of cavity formation and association of inert gas solutes. The connection of information theory to statistical thermodynamics provides a basis for clarification of hydrophobic effects. The simplicity and flexibility of the approach suggest that it should permit applications to conformational equilibria of nonpolar solutes and hydrophobic residues in biopolymers.

Structure-activity relationships derived by machine learning: the use of atoms and their bond connectivities to predict mutagenicity by inductive logic programming.

We present a general approach to forming structure-activity relationships (SARs). This approach is based on representing chemical structure by atoms and their bond connectivities in combination with the inductive logic programming (ILP) algorithm PROGOL. Existing SAR methods describe chemical structure by using attributes which are general properties of an object. It is not possible to map chemical structure directly to attribute-based descriptions, as such descriptions have no internal organization. A more natural and general way to describe chemical structure is to use a relational description, where the internal construction of the description maps that of the object described. Our atom and bond connectivities representation is a relational description. ILP algorithms can form SARs with relational descriptions. We have tested the relational approach by investigating the SARs of 230 aromatic and heteroaromatic nitro compounds. These compounds had been split previously into two subsets, 188 compounds that were amenable to regression and 42 that were not. For the 188 compounds, a SAR was found that was as accurate as the best statistical or neural network-generated SARs. The PROGOL SAR has the advantages that it did not need the use of any indicator variables handcrafted by an expert, and the generated rules were easily comprehensible. For the 42 compounds, PROGOL formed a SAR that was significantly (P < 0.025) more accurate than linear regression, quadratic regression, and back-propagation. This SAR is based on an automatically generated structural alert for mutagenicity.