Pitch perception: A dynamical-systems perspective

Two and a half millennia ago Pythagoras initiated the scientific study of the pitch of sounds; yet our understanding of the mechanisms of pitch perception remains incomplete. Physical models of pitch perception try to explain from elementary principles why certain physical characteristics of the stimulus lead to particular pitch sensations. There are two broad categories of pitch-perception models: place or spectral models consider that pitch is mainly related to the Fourier spectrum of the stimulus, whereas for periodicity or temporal models its characteristics in the time domain are more important. Current models from either class are usually computationally intensive, implementing a series of steps more or less supported by auditory physiology. However, the brain has to analyze and react in real time to an enormous amount of information from the ear and other senses. How is all this information efficiently represented and processed in the nervous system? A proposal of nonlinear and complex systems research is that dynamical attractors may form the basis of neural information processing. Because the auditory system is a complex and highly nonlinear dynamical system, it is natural to suppose that dynamical attractors may carry perceptual and functional meaning. Here we show that this idea, scarcely developed in current pitch models, can be successfully applied to pitch perception.

Characterization of the transposition pattern of the Ac element in Arabidopsis thaliana using endonuclease I-SceI

We have investigated physical distances and directions of transposition of the maize transposable element Ac in Arabidopsis thaliana. We prepared a transferred DNA (T-DNA) construct that carried a non-autonomous derivative of Ac with a site for cleavage by endonuclease I-SceI (designated dAc-I-RS element). Another cleavage site was also introduced into the T-DNA region outside dAc-I-RS. Three transgenic Arabidopsis plants were generated, each of which had a single copy of the T-DNA at a different chromosomal location. These transgenic plants were crossed with the Arabidopsis that carried the gene for Ac transposase and progeny in which dAc-I-RS had been transposed were isolated. After digestion of the genomic DNA of these progeny with endonuclease I-SceI, sizes of segment of DNA were determined by pulse-field gel electrophoresis. We also performed linkage analysis for the transposed elements and sites of mutations near the elements. Our results showed that 50% of all transposition events had occurred within 1,700 kb on the same chromosome, with 35% within 200 kb, and that the elements transposed in both directions on the chromosome with roughly equal probability. The data thus indicate that the Ac–Ds system is most useful for tagging of genes that are present within 200 kb of the chromosomal site of Ac in Arabidopsis. In addition, determination of the precise localization of the transposed dAc-I-RS element should definitely assist in map-based cloning of genes around insertion sites.

Somatic and germ cell parasitism in a colonial ascidian: Possible role for a highly polymorphic allorecognition system

A colonial protochordate, Botryllus schlosseri, undergoes a natural transplantation reaction in the wild that results alternatively in colony fusion (chimera formation) or inflammatory rejection. A single, highly polymorphic histocompatibility locus (called Fu/HC) is responsible for rejection versus fusion. Gonads are seeded and gametogenesis can occur in colonies well after fusion, and involves circulating germ-line progenitors. Buss proposed that colonial organisms might develop self/non-self histocompatibility systems to limit the possibility of interindividual germ cell “parasitism” (GCP) to histocompatible kin [Buss, L. W. (1982) Proc. Natl. Acad. Sci. USA 79, 5337–5341 and Buss, L. W. (1987) The Evolution of Individuality (Princeton Univ. Press, Princeton]. Here we demonstrate in laboratory and field experiments that both somatic cell and (more importantly) germ-line parasitism are a common occurrence in fused chimeras. These experiments support the tenet in Buss’s hypothesis that germ cell and somatic cell parasitism can occur in fused chimeras and that a somatic appearance may mask the winner of a gametic war. They also provide an interesting challenge to develop formulas that describe the inheritance of competing germ lines rather than competing individuals. The fact that fused B. schlosseri have higher rates of GCP than unfused colonies additionally provides a rational explanation for the generation and maintenance of a high degree of Fu/HC polymorphism, largely limiting GCP to sibling offspring.

The vibrational energy flow transition in organic molecules: Theory meets experiment

Most large dynamical systems are thought to have ergodic dynamics, whereas small systems may not have free interchange of energy between degrees of freedom. This assumption is made in many areas of chemistry and physics, ranging from nuclei to reacting molecules and on to quantum dots. We examine the transition to facile vibrational energy flow in a large set of organic molecules as molecular size is increased. Both analytical and computational results based on local random matrix models describe the transition to unrestricted vibrational energy flow in these molecules. In particular, the models connect the number of states participating in intramolecular energy flow to simple molecular properties such as the molecular size and the distribution of vibrational frequencies. The transition itself is governed by a local anharmonic coupling strength and a local state density. The theoretical results for the transition characteristics compare well with those implied by experimental measurements using IR fluorescence spectroscopy of dilution factors reported by Stewart and McDonald [Stewart, G. M. & McDonald, J. D. (1983) J. Chem. Phys. 78, 3907–3915].

Complexity, contingency, and criticality.

Complexity originates from the tendency of large dynamical systems to organize themselves into a critical state, with avalanches or "punctuations" of all sizes. In the critical state, events which would otherwise be uncoupled become correlated. The apparent, historical contingency in many sciences, including geology, biology, and economics, finds a natural interpretation as a self-organized critical phenomenon. These ideas are discussed in the context of simple mathematical models of sandpiles and biological evolution. Insights are gained not only from numerical simulations but also from rigorous mathematical analysis.