Porosity Controls Spread of Excitation in Tectorial Membrane Traveling Waves

Cochlear frequency selectivity plays a key role in our ability to understand speech, and is widely believed to be associated with cochlear amplification. However, genetic studies targeting the tectorial membrane (TM) have demonstrated both sharper and broader tuning with no obvious changes in hair bundle or somatic motility mechanisms. For example, cochlear tuning of Tectb^–/– mice is significantly sharper than that of Tecta^Y1870C/+ mice, even though TM stiffnesses are similarly reduced relative to wild-type TMs. Here we show that differences in TM viscosity can account for these differences in tuning. In the basal cochlear turn, nanoscale pores of Tecta^Y1870C/+ TMs are significantly larger than those of Tectb^–/– TMs. The larger pore size reduces shear viscosity (by ∼70%), thereby reducing traveling wave speed and increasing spread of excitation. These results demonstrate the previously unrecognized importance of TM porosity in cochlear and neural tuning.     

Traveling Waves and Spread Rates for a West Nile Virus Model

A reaction–diffusion model for the spatial spread of West Nile virus is developed and analysed. Infection dynamics are based on a modified version of a model for cross infection between birds and mosquitoes (Wonham et al., 2004, An epidemiological model for West-Nile virus: Invasion analysis and control application. Proc. R. Soc. Lond. B 271), and diffusion terms describe movement of birds and mosquitoes. Working with a simplified version of the model, the cooperative nature of cross-infection dynamics is utilized to prove the existence of traveling waves and to calculate the spatial spread rate of infection. Comparison theorem results are used to show that the spread rate of the simplified model may provide an upper bound for the spread rate of a more realistic and complex version of the model.     

The Analysis of Synaptically Generated Traveling Waves

Mathematical and computational models for the propagation of activity in excitatorily coupled neurons are simulated and analyzed. The basic measurable quantity—velocity—is found for a wide class of models. Numerical bifurcation techniques, asymptotic analysis, and numerical simulations are used to show that there are distinct scaling laws for the velocity as a function of a variety of parameters. In particular, the obvious linear relationships between speed and spatial spread or synaptic decay rate are shown. More surprisingly, it is shown that the velocity scales as a power law with synaptic coupling strength and that the exponent is dependent only on the rising phase of the synapse.     

Frequency-Dependent Properties of the Tectorial Membrane Facilitate Energy Transmission and Amplification in the Cochlea

The remarkable sensitivity, frequency selectivity, and dynamic range of the mammalian cochlea relies on longitudinal transmission of minuscule amounts of energy as passive, pressure-driven, basilar membrane (BM) traveling waves. These waves are actively amplified at frequency-specific locations by a mechanism that involves interaction between the BM and another extracellular matrix, the tectorial membrane (TM). From mechanical measurements of isolated segments of the TM, we made the important new (to our knowledge) discovery that the stiffness of the TM is reduced when it is mechanically stimulated at physiologically relevant magnitudes and at frequencies below their frequency place in the cochlea. The reduction in stiffness functionally uncouples the TM from the organ of Corti, thereby minimizing energy losses during passive traveling-wave propagation. Stiffening and decreased viscosity of the TM at high stimulus frequencies can potentially facilitate active amplification, especially in the high-frequency, basal turn, where energy loss due to internal friction within the TM is less than in the apex. This prediction is confirmed by neural recordings from several frequency regions of the cochlea.     

The Spread of Excitation in the Embryonic Chick Heart

The spread of excitation in embryonic chick hearts, ranging in age from 7 to 20 days, was studied with both intracellular and extracellular electrodes. Evidence that the delay in ventricular excitation could be attributed to the cells of the entire atrioventricular (AV) ring was obtained, in part, from sagittal sections of the heart. In the intact preparation, uniform propagation occurred throughout the atrial roof at an apparent conduction velocity of 0.4 to 0.5 meter/sec. Delay of impulse propagation was localized in a very narrow band of tissue which extended across the AV ring. The apparent conduction velocity of this tissue was between 0.003 and 0.005 meter/sec. Both normal and retrograde propagation revealed the spread of conduction across the AV ring to be decremental in nature. This finding was supported by high frequency stimulation experiments which gave rise to AV block localized in the cells of the AV ring. Cardiac rhythmicity and AV transmission were responsive to acetylcholine and norepinephrine in much the same manner as in the adult mammalian heart. The present findings are in support of the hypothesis that the embryonic AV ring is the functional counterpart of the adult AV node.     

混合拟单调系统行波解的存在性

运用单调迭代方法,证明了混合拟单调系统的行波解的存在性．当反应扩散系。统的反应函数是混合拟单调函数时,如果选取一对合适的耦合上下解作为迭代初值,则迭代序列将收敛到一对拟解．而且在这对拟解之间存在系统的行波解．     

Effect of the Attachment of the Tectorial Membrane on Cochlear Micromechanics and Two-Tone Suppression

The mechanical stimulation of the outer hair cell hair bundle (HB) is a key step in nonlinear cochlear amplification. We show how two-tone suppression (TTS), a hallmark of cochlear nonlinearity, can be used as an indirect measure of HB stimulation. Using two different nonlinear computational models of the cochlea, we investigate the effect of altering the mechanical load applied by the tectorial membrane (TM) on the outer hair cell HB. In the first model (TM-A model), the TM is attached to the spiral limbus (as in wild-type animals); in the second model (TM-D model), the TM is detached from the spiral limbus (mimicking the cochlea of Otoa^EGFP/EGFP mutant mice). As in recent experiments, model simulations demonstrate that the absence of the TM attachment does not preclude cochlear amplification. However, detaching the TM alters the mechanical load applied by the TM on the HB at low frequencies and therefore affects TTS by low-frequency suppressors. For low-frequency suppressors, the suppression threshold obtained with the TM-A model corresponds to a constant suppressor displacement on the basilar membrane (as in experiments with wild-type animals), whereas it corresponds to a constant suppressor velocity with the TM-D model. The predictions with the TM-D model could be tested by measuring TTS on the basilar membrane of the Otoa^EGFP/EGFP mice to improve our understanding of the fundamental workings of the cochlea.     

带时滞互惠模型的稳定性和行波解的存在性

本文建立了一类空间非局部带时滞影响的互惠生物种群系统模型.前部分利用线性化方法证明了该模型的简单动力学行为,即证明了零平衡点和两个边界平衡点都是不稳定的,唯一的正平衡点是稳定的,同时还用Redlinger上下解方法得出了该模型的初边值问题存在唯一的正则解;后部分则证明了该反应扩散系统连接零平衡点和正平衡点的行波解的存在性.     

Effect of the Attachment of the Tectorial Membrane on Cochlear Micromechanics and Two-Tone Suppression

The mechanical stimulation of the outer hair cell hair bundle (HB) is a key step in nonlinear cochlear amplification. We show how two-tone suppression (TTS), a hallmark of cochlear nonlinearity, can be used as an indirect measure of HB stimulation. Using two different nonlinear computational models of the cochlea, we investigate the effect of altering the mechanical load applied by the tectorial membrane (TM) on the outer hair cell HB. In the first model (TM-A model), the TM is attached to the spiral limbus (as in wild-type animals); in the second model (TM-D model), the TM is detached from the spiral limbus (mimicking the cochlea of Otoa^EGFP/EGFP mutant mice). As in recent experiments, model simulations demonstrate that the absence of the TM attachment does not preclude cochlear amplification. However, detaching the TM alters the mechanical load applied by the TM on the HB at low frequencies and therefore affects TTS by low-frequency suppressors. For low-frequency suppressors, the suppression threshold obtained with the TM-A model corresponds to a constant suppressor displacement on the basilar membrane (as in experiments with wild-type animals), whereas it corresponds to a constant suppressor velocity with the TM-D model. The predictions with the TM-D model could be tested by measuring TTS on the basilar membrane of the Otoa^EGFP/EGFP mice to improve our understanding of the fundamental workings of the cochlea.     

Collective Fluctuations in the Dynamics of Adaptation and Other Traveling Waves

The dynamics of adaptation are difficult to predict because it is highly stochastic even in large populations. The uncertainty emerges from random genetic drift arising in a vanguard of particularly fit individuals of the population. Several approaches have been developed to analyze the crucial role of genetic drift on the expected dynamics of adaptation, including the mean fitness of the entire population, or the fate of newly arising beneficial deleterious mutations. However, little is known about how genetic drift causes fluctuations to emerge on the population level, where it becomes palpable as variations in the adaptation speed and the fitness distribution. Yet these phenomena control the decay of genetic diversity and variability in evolution experiments and are key to a truly predictive understanding of evolutionary processes. Here, we show that correlations induced by these emergent fluctuations can be computed at any arbitrary order by a suitable choice of a dynamical constraint. The resulting linear equations exhibit fluctuation-induced terms that amplify short-distance correlations and suppress long-distance ones. These terms, which are in general not small, control the decay of genetic diversity and, for wave-tip dominated (“pulled”) waves, lead to anticorrelations between the tip of the wave and the lagging bulk of the population. While it is natural to consider the process of adaptation as a branching random walk in fitness space subject to a constraint (due to finite resources), we show that other traveling wave phenomena in ecology and evolution likewise fall into this class of constrained branching random walks. Our methods, therefore, provide a systematic approach toward analyzing fluctuations in a wide range of population biological processes, such as adaptation, genetic meltdown, species invasions, or epidemics.     

Porosity of the Yeast Cell Wall and Membrane

The limiting sizes of molecules that can permeate the intact cell wall and protoplast membrane of Saccharomyces cerevisiae were determined from the inflection points in a triphasic pattern of passive equilibrium uptake values obtained with a series of inert probing molecules varying in molecular size. In the phase identified with the yeast protoplast, the uptake-exclusion threshold corresponded to a monodisperse ethylene glycol of molecular weight = 110 and Einstein-Stokes hydrodynamic radius (r(ES)) = 0.42 nm. In the cell wall phase, the threshold corresponded to a polydisperse polyethylene glycol of number-average molecular weight ( M(n)) = 620 and average radius (r(ES)) = 0.81 nm. The third phase corresponded to complete exclusion of larger molecules. The assessment of cell wall porosity was confirmed by use of a second method involving analytical gel chromatographic analyses of the molecular weight distribution for a single polydisperse polyglycol before and after uptake by the cells, which indicated a quasi-monodisperse threshold for the cell wall of M(n) = 760 and r(ES) = 0.89 nm. The results were reconciled with two situations in which much larger protein molecules previously have been reported able to penetrate the yeast cell wall.     

The Architecture of Traveling Actin Waves Revealed by Cryo-Electron Tomography

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Modified Protein Expression in the Tectorial Membrane of the Cochlea Reveals Roles for the Striated Sheet Matrix

The tectorial membrane (TM) of the mammalian cochlea is a complex extracellular matrix which, in response to acoustic stimulation, displaces the hair bundles of outer hair cells (OHCs), thereby initiating sensory transduction and amplification. Here, using TM segments from the basal, high-frequency region of the cochleae of genetically modified mice (including models of human hereditary deafness) with missing or modified TM proteins, we demonstrate that frequency-dependent stiffening is associated with the striated sheet matrix (SSM). Frequency-dependent stiffening largely disappeared in all three TM mutations studied where the SSM was absent either entirely or at least from the stiffest part of the TM overlying the OHCs. In all three TM mutations, dissipation of energy is decreased at low (<8 kHz) and increased at high (>8 kHz) stimulus frequencies. The SSM is composed of polypeptides carrying fixed charges, and electrostatic interaction between them may account for frequency-dependent stiffness changes in the material properties of the TM. Through comparison with previous in vivo measurements, it is proposed that implementation of frequency-dependent stiffening of the TM in the OHC attachment region facilitates interaction among tones, backward transmission of energy, and amplification in the cochlea.     

Traveling Theta Waves along the Entire Septotemporal Axis of the Hippocampus

A topographical relationship exists between the hippocampus-entorhinal cortex and the neocortex. However, it is not known how these anatomical connections are utilized during information exchange and behavior. We recorded theta oscillations along the entire extent of the septotemporal axis of the hippocampal CA1 pyramidal layer. While the frequency of theta oscillation remained same along the entire long axis, the amplitude and coherence between recording sites decreased from dorsal to ventral hippocampus (VH). Theta phase shifted monotonically with distance along the longitudinal axis, reaching ～180° between the septal and temporal poles. The majority of concurrently recorded units were phase-locked to the local field theta at all dorsoventral segments. The power of VH theta had only a weak correlation with locomotion velocity, and its amplitude varied largely independently from theta in the dorsal part. Thus, theta oscillations can temporally combine or segregate neocortical representations along the septotemporal axis of the hippocampus.     

Experimental and Theoretical Explorations of Traveling Waves and Tuning in the Bushcricket Ear

The ability to detect airborne sound is essential for many animals. Examples from the inner ear of mammals and bushcrickets demonstrate that similar detection strategies evolved in taxonomically distant species. Both mammalian and bushcricket ears possess a narrow strip of sensory tissue that exhibits an anatomical gradient and traveling wave motion responses used for frequency discrimination. We measured pressure and motion in the bushcricket ear to investigate physical properties, stiffness, and mass, which govern the mechanical responses to sound. As in the mammalian cochlea, sound-induced fluid pressure and motion responses were tonotopically organized along the longitudinal axis of the crista acustica, the bushcricket’s hearing organ. The fluid pressure at the crista and crista motion were used to calculate the acoustic impedance of the organ-bounded fluid mass (Z_mass). We used a theoretical wave analysis of wavelength data from a previous study to predict the crista acustica stiffness. The wave analysis also predicts Z_mass, and that result agreed reasonably well with the directly measured Z_mass, lending support to the theoretical wave analysis. The magnitude of the crista stiffness was similar to basilar membrane stiffness in mammals, and as in mammals, the stiffness decreased from the high-frequency to the low-frequency region. At a given location, the stiffness increased with increasing frequency, corresponding to increasing curvature of the traveling wave (decreasing wavelength), indicating that longitudinal coupling plays a substantial role in determining crista stiffness. This is in contrast to the mammalian ear, in which stiffness is independent of frequency and longitudinal coupling is relatively small.     

On Propagation of Excitation Waves in Moving Media: The FitzHugh-Nagumo Model

Background

Existence of flows and convection is an essential and integral feature of many excitable media with wave propagation modes, such as blood coagulation or bioreactors.

Methods/Results

Here, propagation of two-dimensional waves is studied in parabolic channel flow of excitable medium of the FitzHugh-Nagumo type. Even if the stream velocity is hundreds of times higher that the wave velocity in motionless medium (), steady propagation of an excitation wave is eventually established. At high stream velocities, the wave does not span the channel from wall to wall, forming isolated excited regions, which we called “restrictons”. They are especially easy to observe when the model parameters are close to critical ones, at which waves disappear in still medium. In the subcritical region of parameters, a sufficiently fast stream can result in the survival of excitation moving, as a rule, in the form of “restrictons”. For downstream excitation waves, the axial portion of the channel is the most important one in determining their behavior. For upstream waves, the most important region of the channel is the near-wall boundary layers. The roles of transversal diffusion, and of approximate similarity with respect to stream velocity are discussed.

Conclusions

These findings clarify mechanisms of wave propagation and survival in flow.     

Three-Dimensional Cell Geometry Controls Excitable Membrane Signaling in Dictyostelium Cells

Phosphatidylinositol (3–5)-trisphosphate (PtdInsP3) is known to propagate as waves on the plasma membrane and is related to the membrane-protrusive activities in Dictyostelium and mammalian cells. Although there have been a few attempts to study the three-dimensional (3D) dynamics of these processes, most studies have focused on the dynamics extracted from single focal planes. However, the relation between the dynamics and 3D cell shape remains elusive because of the lack of signaling information about the unobserved part of the membrane. Here, we show that PtdInsP3 wave dynamics are directly regulated by the 3D geometry (i.e., size and shape) of the plasma membrane. By introducing an analysis method that extracts the 3D spatiotemporal activities on the entire cell membrane, we show that PtdInsP3 waves self-regulate their dynamics within the confined membrane area. This leads to changes in speed, orientation, and pattern evolution, following the underlying excitability of the signal transduction system. Our findings emphasize the role of the plasma membrane topology in reaction-diffusion-driven biological systems and indicate its importance in other mammalian systems.     

Regulation Mechanism of Excitation Energy Transfer in Phycobilisome-Thylakoid Membrane Complexes

Regulation mechanism of excitation energy transfer between phycobilisomes (PBS) and the photosynthetic reaction centres was studied by the state transition techniques in PBS-thylakoid membrane complexes. DCMU, betaine, and N-ethylmaleimide were applied to search for the details of energy transfer properties based on the steady fluorescence measurement and individual deconvolution spectra at state 2 or state 1. The closure of photosystem (PS) 2 did not influence on fluorescence yields of PS1, i.e., energy could not spill to PS1 from PS2. When the energy transfer pathway from PBS to PS1 was disturbed, the relative fluorescence yield of PS2 was almost the same as that of PS2 in complexes without treatment. If PBSs were fixed by betaine, the state transition process was restrained. Hence PBS may detach from PS2 and become associated to PS1 at state 2. Our results contradict the proposed "spill-over" or "PBS detachment" models and support the mobile "PBS model".     

一类具有时空时滞的单种群模型行波解的存在性

通过单调迭代和上下解技术,研究了一类具有时空时滞的单物种种群模型行波解的存在性,证明了当时滞充分小时,方程具有连接两个平衡点的波前解,并得到了一些新的结果.