A model for amplification of hair-bundle motion by cyclical binding of Ca2+ to mechanoelectrical-transduction channels

Amplification of auditory stimuli by hair cells augments the sensitivity of the vertebrate inner ear. Cell-body contractions of outer hair cells are thought to mediate amplification in the mammalian cochlea. In vertebrates that lack these cells, and perhaps in mammals as well, active movements of hair bundles may underlie amplification. We have evaluated a mathematical model in which amplification stems from the activity of mechanoelectrical-transduction channels. The intracellular binding of Ca2+ to channels is posited to promote their closure, which increases the tension in gating springs and exerts a negative force on the hair bundle. By enhancing bundle motion, this force partially compensates for viscous damping by cochlear fluids. Linear stability analysis of a six-state kinetic model reveals Hopf bifurcations for parameter values in the physiological range. These bifurcations signal conditions under which the system’s behavior changes from a damped oscillatory response to spontaneous limit-cycle oscillation. By varying the number of stereocilia in a bundle and the rate constant for Ca2+ binding, we calculate bifurcation frequencies spanning the observed range of auditory sensitivity for a representative receptor organ, the chicken’s cochlea. Simulations using prebifurcation parameter values demonstrate frequency-selective amplification with a striking compressive nonlinearity. Because transduction channels occur universally in hair cells, this active-channel model describes a mechanism of auditory amplification potentially applicable across species and hair-cell types.

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.

Genetic supercycles caused by cyclical selection.

Typical behavior of a two-locus genetic system experiencing cyclical selection, includes fixation (in one or both loci) or a stable polymorphic cycle with a period equal to that of environmental changes. By considering the time scale in terms of environmental periods, the last case could be trivially classified as a polymorphic stable point. Here we report on some results showing the complex limiting behavior of diploid population trajectories resulting from selection in a cyclically changing environment. We found that simple cyclical selection could produce genetic supercycles composed of many hundreds of environmental periods.

Recurrent invasion and extinction of a selfish gene

Homing endonuclease genes show super-Mendelian inheritance, which allows them to spread in populations even when they are of no benefit to the host organism. To test the idea that regular horizontal transmission is necessary for the long-term persistence of these genes, we surveyed 20 species of yeasts for the ω-homing endonuclease gene and associated group I intron. The status of ω could be categorized into three states (functional, nonfunctional, or absent), and status was not clustered on the host phylogeny. Moreover, the phylogeny of ω differed significantly from that of the host, strong evidence of horizontal transmission. Further analyses indicate that horizontal transmission is more common than transposition, and that it occurs preferentially between closely related species. Parsimony analysis and coalescent theory suggest that there have been 15 horizontal transmission events in the ancestry of our yeast species, through simulations indicate that this value is probably an underestimate. Overall, the data support a cyclical model of invasion, degeneration, and loss, followed by reinvasion, and each of these transitions is estimated to occur about once every 2 million years. The data are thus consistent with the idea that frequent horizontal transmission is necessary for the long-term persistence of homing endonuclease genes, and further, that this requirement limits these genes to organisms with easily accessible germ lines. The data also show that mitochondrial DNA sequences are transferred intact between yeast species; if other genes do not show such high levels of horizontal transmission, it would be due to lack of selection, rather than lack of opportunity.

Genetic epidemiology of single-nucleotide polymorphisms

On the causal hypothesis, most genetic determinants of disease are single-nucleotide polymorphisms (SNPs) that are likely to be selected as markers for positional cloning. On the proximity hypothesis, most disease determinants will not be included among markers but may be detected through linkage disequilibrium with other SNPs. In that event, allelic association among SNPs is an essential factor in positional cloning. Recent simulation based on monotonic population expansion suggests that useful association does not usually extend beyond 3 kb. This is contradicted by significant disequilibrium at much greater distances, with corresponding reduction in the number of SNPs required for a cost-effective genome scan. A plausible explanation is that cyclical expansions follow population bottlenecks that establish new disequilibria. Data on more than 1,000 locus pairs indicate that most disequilibria trace to the Neolithic, with no apparent difference between haplotypes that are random or selected through a major disease gene. Short duration may be characteristic of alleles contributing to disease susceptibility and haplotypes characteristic of particular ethnic groups. Alleles that are highly polymorphic in all ethnic groups may be older, neutral, or advantageous, in weak disequilibrium with nearby markers, and therefore less useful for positional cloning of disease genes. Significant disequilibrium at large distance makes the number of suitably chosen SNPs required for genome screening as small as 30,000, or 1 per 100 kb, with greater density (including less common SNPs) reserved for candidate regions.

Dynamic localization of a cytoplasmic signal transduction response regulator controls morphogenesis during the Caulobacter cell cycle

We present evidence that a bacterial signal transduction cascade that couples morphogenesis with cell cycle progression is regulated by dynamic localization of its components. Previous studies have implicated two histidine kinases, DivJ and PleC, and the response regulator, DivK, in the regulation of morphogenesis in the dimorphic bacterium Caulobacter crescentus. Here, we show that the cytoplasmic response regulator, DivK, exhibits a dynamic, cyclical localization that culminates in asymmetric distribution of DivK within the two cell types that are characteristic of the Caulobacter cell cycle; DivK is dispersed throughout the cytoplasm of the progeny swarmer cell and is localized to the pole of the stalked cell. The membrane-bound DivJ and PleC histidine kinases, which are asymmetrically localized at the opposite poles of the predivisional cell, control the temporal and spatial localization of DivK. DivJ mediates DivK targeting to the poles whereas PleC controls its release from one of the poles at times and places that are consistent with the activities and location of DivJ and PleC in the late predivisional cell. Thus, dynamic changes in subcellular location of multiple components of a signal transduction cascade may constitute a novel mode of prokaryotic regulation to generate and maintain cellular asymmetry.

Evolution of genome–phenome diversity under environmental stress

The genomic era revolutionized evolutionary biology. The enigma of genotypic-phenotypic diversity and biodiversity evolution of genes, genomes, phenomes, and biomes, reviewed here, was central in the research program of the Institute of Evolution, University of Haifa, since 1975. We explored the following questions. (i) How much of the genomic and phenomic diversity in nature is adaptive and processed by natural selection? (ii) What is the origin and evolution of adaptation and speciation processes under spatiotemporal variables and stressful macrogeographic and microgeographic environments? We advanced ecological genetics into ecological genomics and analyzed globally ecological, demographic, and life history variables in 1,200 diverse species across life, thousands of populations, and tens of thousands of individuals tested mostly for allozyme and partly for DNA diversity. Likewise, we tested thermal, chemical, climatic, and biotic stresses in several model organisms. Recently, we introduced genetic maps and quantitative trait loci to elucidate the genetic basis of adaptation and speciation. The genome–phenome holistic model was deciphered by the global regressive, progressive, and convergent evolution of subterranean mammals. Our results indicate abundant genotypic and phenotypic diversity in nature. The organization and evolution of molecular and organismal diversity in nature at global, regional, and local scales are nonrandom and structured; display regularities across life; and are positively correlated with, and partly predictable by, abiotic and biotic environmental heterogeneity and stress. Biodiversity evolution, even in small isolated populations, is primarily driven by natural selection, including diversifying, balancing, cyclical, and purifying selective regimes, interacting with, but ultimately overriding, the effects of mutation, migration, and stochasticity.