Hanspeter Herzel

Calls out of chaos: the adaptive significance of nonlinear phenomena in mammalian vocal production

Abstract Recent work on human vocal production demonstrates that certain irregular phenomena seen in human pathological voices and baby crying result from nonlinearities in the vocal production system. Equivalent phenomena are quite common in nonhuman mammal vocal repertoires. In particular, bifurcations and chaos are ubiquitous aspects of the normal adult repertoire in many primate species. Here we argue that these phenomena result from properties inherent in the peripheral production mechanism, which allows individuals to generate highly complex and unpredictable vocalizations without requiring equivalently complex neural control mechanisms. We provide examples from the vocal repertoire of rhesus macaques, Macaca mulatta , and other species illustrating the different classes of nonlinear phenomena, and review the concepts from nonlinear dynamics that explicate these calls. Finally, we discuss the evolutionary significance of nonlinear vocal phenomena. We suggest that nonlinear phenomena may subserve individual recognition and the estimation of size or fluctuating asymmetry from vocalizations. Furthermore, neurally ‘cheap’ unpredictability may serve the valuable adaptive function of making chaotic calls difficult to predict and ignore. While noting that nonlinear phenomena are in some cases probably nonadaptive by-products of the physics of the sound-generating mechanism, we suggest that these functional hypotheses provide at least a partial explanation for the ubiquity of nonlinear calls in nonhuman vocal repertoires.

Bifurcations in an asymmetric vocal‐fold model

A two-mass model of vocal-fold vibrations is analyzed with methods from nonlinear dynamics. Bifurcations are located in parameter planes of physiological interest (subglottal pressure, stiffness of the folds). It is shown that a sufficiently large tension imbalance of the left and right vocal fold induces bifurcations to subharmonic regimes, toroidal oscillations, and chaos. The corresponding attractors are characterized by phase portraits, spectra, and next-maximum maps. The relevance of these simulations for voice disorders such as laryngeal paralysis is discussed.

SUBHARMONICS, BIPHONATION, AND DETERMINISTIC CHAOS IN MAMMAL VOCALIZATION

ABSTRACT To establish a framework for discussing mammalian vocalizations, relevant terminology and concepts from the theory of nonlinear dynamics are introduced. It is suggested that a variety of nonlinear phenomena including subharmonics, biphonation, and deterministic chaos are normally occurring phonatory events. The whole spectrum of these phenomena can be found in the repertoire of the African wild dog Lycaon pictus. In addition, examples of nonlinear phenomena in a wide range of other mammalian taxa will be presented. Moreover, some artifacts in sound spectrographic analysis are listed which may be misinterpreted as nonlinear phenomena. Within the framework of nonlinear dynamics, a consistent terminology is proposed and our observations are related to laryngeal sound production mechanisms. Finally, some hypotheses concerning the communicative potential of the described phenomena are discussed.

Molecular insights into human daily behavior

Human beings exhibit wide variation in their timing of daily behavior. We and others have suggested previously that such differences might arise because of alterations in the period length of the endogenous human circadian oscillator. Using dermal fibroblast cells from skin biopsies of 28 subjects of early and late chronotype (11 “larks” and 17 “owls”), we have studied the circadian period lengths of these two groups, as well as their ability to phase-shift and entrain to environmental and chemical signals. We find not only period length differences between the two classes, but also significant changes in the amplitude and phase-shifting properties of the circadian oscillator among individuals with identical “normal” period lengths. Mathematical modeling shows that these alterations could also account for the extreme behavioral phenotypes of these subjects. We conclude that human chronotype may be influenced not only by the period length of the circadian oscillator, but also by cellular components that affect its amplitude and phase. In many instances, these changes can be studied at the molecular level in primary dermal cells.

INTERPRETATION OF BIOMECHANICAL SIMULATIONS OF NORMAL AND CHAOTIC VOCAL FOLD OSCILLATIONS WITH EMPIRICAL EIGENFUNCTIONS

Empirical orthogonal eigenfunctions are extracted from biomechanical simulations of normal and chaotic vocal fold oscillations. For normal phonation, two dominant empirical eigenfunctions capture the vibration patterns of the folds and exhibit a 1:1 entrainment. The eigenfunctions show some correspondence to theoretical low-order normal modes of a simplified, three-dimensional elastic continuum, and to the normal modes of a linearized two-mass model. The eigenfunctions also facilitate a physical interpretation of energy transfer mechanisms in vocal fold dynamics. Subharmonic regimes and chaotic oscillations are observed during simulations of a lax cover, in which case at least three empirical eigenfunctions are necessary to capture the resulting vocal fold oscillations. These chaotic oscillations might be understood in terms of a desynchronization of a few of the low-order modes, and may be related to mechanisms of creaky voice or vocal fry. Furthermore, some of the empirical eigenfunctions captured during complex oscillations correspond to higher-order normal modes described in earlier theoretical work. The empirical eigenfunctions may also be useful in the design of lower-order models (valid over the range for which the empirical eigenfunctions remain more or less constant), and may help facilitate bifurcation analyses of the biomechanical simulation.

Regulation of Clock-Controlled Genes in Mammals.

The complexity of tissue- and day time-specific regulation of thousands of clock-controlled genes (CCGs) suggests that many regulatory mechanisms contribute to the transcriptional output of the circadian clock. We aim to predict these mechanisms using a large scale promoter analysis of CCGs. Our study is based on a meta-analysis of DNA-array data from rodent tissues. We searched in the promoter regions of 2065 CCGs for highly overrepresented transcription factor binding sites. In order to compensate the relatively high GC-content of CCG promoters, a novel background model to avoid a bias towards GC-rich motifs was employed. We found that many of the transcription factors with overrepresented binding sites in CCG promoters exhibit themselves circadian rhythms. Among the predicted factors are known regulators such as CLOCK∶BMAL1, DBP, HLF, E4BP4, CREB, RORα and the recently described regulators HSF1, STAT3, SP1 and HNF-4α. As additional promising candidates of circadian transcriptional regulators PAX-4, C/EBP, EVI-1, IRF, E2F, AP-1, HIF-1 and NF-Y were identified. Moreover, GC-rich motifs (SP1, EGR, ZF5, AP-2, WT1, NRF-1) and AT-rich motifs (MEF-2, HMGIY, HNF-1, OCT-1) are significantly overrepresented in promoter regions of CCGs. Putative tissue-specific binding sites such as HNF-3 for liver, NKX2.5 for heart or Myogenin for skeletal muscle were found. The regulation of the erythropoietin (Epo) gene was analysed, which exhibits many binding sites for circadian regulators. We provide experimental evidence for its circadian regulated expression in the adult murine kidney. Basing on a comprehensive literature search we integrate our predictions into a regulatory network of core clock and clock-controlled genes. Our large scale analysis of the CCG promoters reveals the complexity and extensiveness of the circadian regulation in mammals. Results of this study point to connections of the circadian clock to other functional systems including metabolism, endocrine regulation and pharmacokinetics.

An attractor in a solar time series

A time series analysis of observed solar radio pulsations suggests that there must be a low-dimensional attractor. The power spectrum cannot be interpreted as a superposition of periodic components. Estimates of the maximum Lyapunov exponent and of the Kolmogorov entropy give some indications for a deterministic chaos. In order to study the limitations inherent in small data samples we include data from the Lorenz model and an artificial noise record. Consequences for the physical modelling of the pulsation event are discussed.

10-11 bp periodicities in complete genomes reflect protein structure and DNA folding.

MOTIVATION Completely sequenced genomes allow for detection and analysis of the relatively weak periodicities of 10-11 basepairs (bp). Two sources contribute to such signals: correlations in the corresponding protein sequences due to the amphipatic character of alpha-helices and the folding of DNA (nucleosomal patterns, DNA supercoiling). Since the topological state of genomic DNA is of importance for its replication, recombination and transcription, there is an immediate interest to obtain information about the supercoiled state from sequence periodicities. RESULTS We show that correlations within proteins affect mainly the oscillations at distances below 35 bp. The long-ranging correlations up to 100 bp reflect primarily DNA folding. For the yeast genome these oscillations are consistent in detail with the chromatin structure. For eubacteria and archaea the periods deviate significantly from the 10.55 bp value for free DNA. These deviations suggest that while a period of 11 bp in bacteria reflects negative supercoiling, the significantly different period of thermophilic archaea close to 10 bp corresponds to positive supercoiling of thermophilic archaeal genomes. AVAILABILITY Protein sets and C programs for the calculation of correlation functions are available on request from the authors (see http://itb.biologie.hu-berlin.de).

Measuring correlations in symbol sequences

The paper is devoted to relations between correlation functions and mutual information. It is shown that, in sequences over an alphabet of λ symbols, statistical dependences are measured by (λ − 1)2 independent parameters. However, not all of them can be determined by autocorrelation functions. Appropriate sets of correlation functions (including crosscorrelations) are introduced, which allow the detection of all dependences. The results are exemplified for binary, ternary, and quaternary symbol sequences. As an application, it is discussed that a nonuniform codon usage in protein-coding DNA sequences introduces periodic correlations even at distances in the order of 1000 base pairs.

Effects of sequestration on signal transduction cascades

The building blocks of most signal transduction pathways are pairs of enzymes, such as kinases and phosphatases, that control the activity of protein targets by covalent modification. It has previously been shown [Goldbeter A & Koshland DE (1981) Proc Natl Acad Sci USA78, 6840–6844] that these systems can be highly sensitive to changes in stimuli if their catalysing enzymes are saturated with their target protein substrates. This mechanism, termed zero‐order ultrasensitivity, may set thresholds that filter out subthreshold stimuli. Experimental data on protein abundance suggest that the enzymes and their target proteins are present in comparable concentrations. Under these conditions a large fraction of the target protein may be sequestrated by the enzymes. This causes a reduction in ultrasensitivity so that the proposed mechanism is unlikely to account for ultrasensitivity under the conditions present in most in vivo signalling cascades. Furthermore, we show that sequestration changes the dynamics of a covalent modification cycle and may account for signal termination and a sign‐sensitive delay. Finally, we analyse the effect of sequestration on the dynamics of a complex signal transduction cascade: the mitogen‐activated protein kinase (MAPK) cascade with negative feedback. We show that sequestration limits ultrasensitivity in this cascade and may thereby abolish the potential for oscillations induced by negative feedback.