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.

Ultrafast diffraction and structural dynamics: The nature of complex molecules far from equilibrium

Studies of molecular structures at or near their equilibrium configurations have long provided information on their geometry in terms of bond distances and angles. Far-from-equilibrium structures are relatively unknown—especially for complex systems—and generally, neither their dynamics nor their average geometries can be extrapolated from equilibrium values. For such nonequilibrium structures, vibrational amplitudes and bond distances play a central role in phenomena such as energy redistribution and chemical reactivity. Ultrafast electron diffraction, which was developed to study transient molecular structures, provides a direct method for probing the nature of complex molecules far from equilibrium. Here we present our ultrafast electron diffraction observations of transient structures for two cyclic hydrocarbons. At high internal energies of ≈4 eV, these molecules display markedly different behavior. For 1,3,5-cycloheptatriene, excitation results in the formation of hot ground-state structures with bond distances similar to those of the initial structure, but with nearly three times the average vibrational amplitude. Energy is redistributed within 5 ps, but with a negative temperature characterizing the nonequilibrium population. In contrast, the ring-opening reaction of 1,3-cyclohexadiene is shown to result in hot structures with a C—C bond distance of over 1.7 Å, which is 0.2 Å away from any expected equilibrium value. Even up to 400 ps, energy remains trapped in large-amplitude motions comprised of torsion and asymmetric stretching. These studies promise a new direction for studying structural dynamics in nonequilibrium complex systems.

Horizontal gene transfer among genomes: The complexity hypothesis

Increasingly, studies of genes and genomes are indicating that considerable horizontal transfer has occurred between prokaryotes. Extensive horizontal transfer has occurred for operational genes (those involved in housekeeping), whereas informational genes (those involved in transcription, translation, and related processes) are seldomly horizontally transferred. Through phylogenetic analysis of six complete prokaryotic genomes and the identification of 312 sets of orthologous genes present in all six genomes, we tested two theories describing the temporal flow of horizontal transfer. We show that operational genes have been horizontally transferred continuously since the divergence of the prokaryotes, rather than having been exchanged in one, or a few, massive events that occurred early in the evolution of prokaryotes. In agreement with earlier studies, we found that differences in rates of evolution between operational and informational genes are minimal, suggesting that factors other than rate of evolution are responsible for the observed differences in horizontal transfer. We propose that a major factor in the more frequent horizontal transfer of operational genes is that informational genes are typically members of large, complex systems, whereas operational genes are not, thereby making horizontal transfer of informational gene products less probable (the complexity hypothesis).

A meanfield approach to the thermodynamics of a protein-solvent system with application to the oligomerization of the tumor suppressor p53

The thermodynamic stability and oligomerization status of the tumor suppressor p53 tetramerization domain have been studied experimentally and theoretically. A series of hydrophilic mutations at Met-340 and Leu-344 of human p53 were designed to disrupt the hydrophobic dimer–dimer interface of the tetrameric oligomerization domain of p53 (residues 325–355). Meanfield calculations of the free energy of the solvated mutants as a function of interdimer distance were compared with experimental data on the thermal stability and oligomeric state (tetramer, dimer, or equilibrium mixture of both) of each mutant. The calculations predicted a decreasing stability and oligomeric state for the following amino acids at residue 340: Met (tetramer) > Ser Asp, His, Gln, > Glu, Lys (dimer), whereas the experimental results showed the following order: Met (tetramer) > Ser > Gln > His, Lys > Asp, Glu (dimers). For residue 344, the calculated trend was Leu (tetramer) > Ala > Arg, Gln, Lys (dimer), and the experimental trend was Leu (tetramer) > Ala, Arg, Gln, Lys (dimer). The discrepancy for the lysine side chain at residue 340 is attributed to the dual nature of lysine, both hydrophobic and charged. The incorrect prediction of stability of the mutant with Asp at residue 340 is attributed to the fact that within the meanfield approach, we use the wild-type backbone configuration for all mutants, but low melting temperatures suggest a softening of the α-helices at the dimer–dimer interface. Overall, this initial application of meanfield theory toward a protein-solvent system is encouraging for the application of the theoretical model to more complex systems.

Signals and signs in the nervous system: The dynamic anatomy of electrical activity is probably information-rich

The dichotomy between two groups of workers on neuroelectrical activity is retarding progress. To study the interrelations between neuronal unit spike activity and compound field potentials of cell populations is both unfashionable and technically challenging. Neither of the mutual disparagements is justified: that spikes are to higher functions as the alphabet is to Shakespeare and that slow field potentials are irrelevant epiphenomena. Spikes are not the basis of the neural code but of multiple codes that coexist with nonspike codes. Field potentials are mainly information-rich signs of underlying processes, but sometimes they are also signals for neighboring cells, that is, they exert influence. This paper concerns opportunities for new research with many channels of wide-band (spike and slow wave) recording. A wealth of structure in time and three-dimensional space is different at each scale—micro-, meso-, and macroactivity. The depth of our ignorance is emphasized to underline the opportunities for uncovering new principles. We cannot currently estimate the relative importance of spikes and synaptic communication vs. extrasynaptic graded signals. In spite of a preponderance of literature on the former, we must consider the latter as probably important. We are in a primitive stage of looking at the time series of wide-band voltages in the compound, local field, potentials and of choosing descriptors that discriminate appropriately among brain loci, states (functions), stages (ontogeny, senescence), and taxa (evolution). This is not surprising, since the brains in higher species are surely the most complex systems known. They must be the greatest reservoir of new discoveries in nature. The complexity should not deter us, but a dose of humility can stimulate the flow of imaginative juices.

Magnetic resonance microscopy and spectroscopy reveal kinetics of cryoprotectant permeation in a multicompartmental biological system.

Successful cryopreservation of most multicompartmental biological systems has not been achieved. One prerequisite for success is quantitative information on cryoprotectant permeation into and amongst the compartments. This report describes direct measurements of cryoprotectant permeation into a multicompartmental system using chemical shift selective magnetic resonance (MR) microscopy and MR spectroscopy. We used the developing zebrafish embryo as a model for studying these complex systems because these embryos are composed of two membrane-limited compartments: (i) a large yolk (surrounded by the yolk syncytial layer) and (ii) differentiating blastoderm cells (each surrounded by a plasma membrane). MR images of the spatial distribution of three cryoprotectants (dimethyl sulfoxide, propylene glycol, and methanol) demonstrated that methanol permeated the entire embryo within 15 min. In contrast, the other cryoprotectants exhibited little or no permeation over 2.5 h. MR spectroscopy and microinjections of cryoprotectants into the yolk inferred that the yolk syncytial layer plays a critical role in limiting the permeation of some cryoprotectants throughout the embryo. This study demonstrates the power of MR technology combined with micromanipulation for elucidating key physiological factors in cryobiology.

Determination of the distance between two spin labels attached to a macromolecule.

An EPR "spectroscopic ruler" was developed using a series of alpha-helical polypeptides, each modified with two nitroxide spin labels. The EPR line broadening due to electron-electron dipolar interactions in the frozen state was determined using the Fourier deconvolution method. These dipolar spectra were then used to estimate the distances between the two nitroxides separated by 8-25 A. Results agreed well with a simple alpha-helical model. The standard deviation from the model system was 0.9 A in the range of 8-25 A. This technique is applicable to complex systems such as membrane receptors and channels, which are difficult to access with high-resolution NMR or x-ray crystallography, and is expected to be particularly useful for systems for which optical methods are hampered by the presence of light-interfering membranes or chromophores.

Complex dynamics of multilocus systems subjected to cyclical selection.

Earlier we have shown that oscillations with a long period ("supercycles") may arise in two-locus systems experiencing cyclical selection with a short period. However, this mode of complex limiting behavior appeared to be possible for narrow ranges of parameters. Here we demonstrate that a multilocus system subjected to stabilizing selection with cyclically moving optimum can generate ubiquitous complex limiting behavior including supercycles, T-cycles, and chaotic-like phenomena. This mode of multilocus dynamics far exceeds the potential attainable under ordinary selection models resulting in simple behavior. It may represent a novel evolutionary mechanism increasing genetic diversity over long-term time periods.