A new quantitative model of total endolymph flow in the system of semicircular ducts

1. A new concept of endolymph flow in the vertebrate vestibular system is presented. This approach describes quantitatively the flow in the entire system of three semicircular ducts interconnected by the utriculus and the crus commune. This approach is quite distinct from the classical theory in which the labyrinth is generally conceived to consist of three separate duct circuits. 2. The present approach shows the following set of distinct differences to the classical view: (a) In a labyrinth composed of three ducts perpendicular to each other the flow is non-zero in the other ducts when the labyrinth is rotated in the plane of a particular duct. (b) In a labyrinth with two equal ducts and with the duct planes under approximately 73 degrees the flow in one duct is zero when the rotation takes place in the plane of the other duct. Previous measurements of duct angles reflect this value surprisingly well. An obtuse or sharp angle between duct planes can lead to better performance of a particular labyrinth because the "external impulses" in the different ducts may amplify or compensate each other. (c) The behaviour of the flow in the entire labyrinth is a non-linear function of direction or rotation (cf. points (d), (e]. (d) Six time constants for the entire labyrinth can be distinguished (three long, three short); the flow in a particular duct is composed of six terms with these time constants. The composition of this flow and thus the relative importance of the terms depends on the positioning of the labyrinth with respect to the rotation vector. (e) The time constants also depend, for different labyrinths, on a shared influence of the dimensions of the ducts and the elastic properties of all three cupulae. (f) The forces in a particular duct depend also on the amount of motion the fluid will acquire in the other ducts. (g) The sensitivity of a particular duct depends also on the dimensions of the other parts in the vestibular system. 3. Equations for a system consisting of two ducts and for the classical single duct system are also given. Both systems are special cases of the three-duct system. The single duct equations are equivalent with equations given by Oman (1980) and Oman et al. (1987) which include the contribution of a wide utriculus. 4. The present theory of endolymph flow is mainly supported by the outcome of previously performed experiments concerning time constants and rotation of human subjects in different planes.(ABSTRACT TRUNCATED AT 400 WORDS)     

Optimization of the mechanical performance of a two-duct semicircular duct system--part 1: dynamics and duct dimensions

The classical representation of the semicircular duct system consists of three separate duct circuits. The ducts are, however, in reality, hydrodynamically interconnected. Muller & Verhagen (1988a,b) derived equations for the mechanical behaviour of an interconnected system with three ducts (anterior, posterior and horizontal). An analytical solution of these equations would, however, be too complex to provide surveyable formulae. A system of two interconnected ducts avoids this complexity whilst keeping the essentials of the coupling of ducts intact. The solution of the equation of motion leads to expressions for time constants and maximal endolymph excursions which are functions of morphological parameters, viz. the ratios of radii (gamma) and lengths (lambda) of the common vestibular part (crus commune or utriculus) and the ducts. The system possesses two short time constants which are shown to have similar values. The maximum endolymph displacements in the two ducts after a steplike stimulus are the products of the respective initial velocities and combinations of time constants. The initial velocities depend strongly on the position of the labyrinth with respect to the excitating rotation vector. Measured data of gamma and lambda are compared with the theoretical results. For gamma, excellent agreement was found. lambda is treated elsewhere.     

Optimization of the mechanical performance of a two-duct semicircular duct system--part 3: the positioning of the ducts in the head

In the majority of vertebrates, the horizontal duct of the vestibular system lies approximately in the yawing plane of the head. The positioning of the vertical ducts, however, is not in the pitch- and roll planes but the vertical ducts generally lie under an angle of about 30-45 degrees relative to the medial plane. Using the equations for a hydrodynamically interconnected two-duct system, optimal positions of the vertical and horizontal ducts in different vertebrate groups can be derived. It was stated that the mean response of the vertical ducts should be optimized. This leads to a symmetrical positioning of the vertical ducts with respect to the medial plane. In all observed vertebrate groups, a solution of mu =(pi-alpha)/2 is found (mu is the angle of the vertical ducts relative to the medial plane, alpha is the angle between the vertical duct planes). For alpha=90 degrees, this provides an equal sensitivity for pitch- and roll- movements. For alpha>90 degrees, a larger sensitivity for pitch movements is obtained, at the expense of a lower sensitivity for roll movements. It is argued that the angle alpha between the vertical ducts may vary from 90 to 120 degrees. In most vertebrates, the centre of mass is stabilized by e.g. fins, tri- or quadrupedal stability, a crawling body or upside-down resting positions (e.g. bats). Birds are generally biped, so in walking they are also rather sensitive to roll. These features are related to labyrinth positioning in the head.     

Non-locality in biological systems results from hierarchy

The concept of non-locality is deduced from a new concept for biological systems, the functional interaction. It is shown that a biological system, which is expressed in terms of functional interactions, can be constructed as a hierarchical system, the dynamics of which are represented by a non-local field at each level of organization. The two following constraints: continuous representation of state variables and hierarchy of the system, result in non-locality, i.e., a space property according to which the system depends on mechanisms that are located elsewhere in the space. Concepts and theory are illustrated in the case of the nervous system, where two levels of organization are considered, the level of neurons and the level of synapses. Non-local versus local field operators are discussed, and an interpretation of the field equation terms is proposed. A general formulation of non-local operators for hierarchical systems is given.     

广义Lotke-Volterra生态模型的非线性奇摄动近似解

非线性奇摄动问题在国际学术界中是一个重要的研究对象。它涉及到许多学科。在一些生态现象中,原始的研究方法只是采取某些简单观察和统计数据来得到结论。但是它对生态现象的实质的研究达不到效果。近来在国际上提出了研究生态学的动力学方法,即人们首先把它归化为代表它的现象本质的微分方程的模型,然后用数学方法来求解对应的方程,最后研究关于生物和数学理论的动力学方面的规律。目前,非线性摄动问题已经被广泛地研究。许多学者已经研究了一些近似理论。近似求解方法已被发展,包括平均法,边界层法,匹配渐近展开和多尺度法等等。研究非线性广义Lotke-Volterra捕食-被捕食生态模型,一个简单而有效的摄动方法被应用到捕食-被捕食生态模型。提出了捕食-被捕食的一个模型,它是一个微分方程系统,并用小的正参数按幂级数展开未知函数,然后得到关于幂级数的系数的方程,并求出它们的解。于是利用摄动方法得到了原问题解的渐近展开式。得到了它是原模型解是一个好的近似的结论,它是一个解析展开式并且能保持其解析运算。最后,给出了一个对应的例子,它说明得到的解具有很好的精度。     

Steady-state electrodiffusion. Scaling, exact solution for ions of one charge, and the phase plane.

This is the first of two papers dealing with electrodiffusion theory (the Nernst-Planck equation coupled with Gauss's law) and its application to the current-voltage behavior of squid axon. New developments in the exact analysis of the steady-state electrodiffusion problem presented here include (a) a scale transformation that connects a given solution to an infinity of other solutions, suggesting the po-sibility of direct comparison of electrical data for membranes with different thicknesses and other properties; (b) a first-integral relation between the electric field and ion densities more general than analogous relations previously reported, and (c) an exact solution for the homovalent system, i.e., a membrane system permeated by various ion species of the same charge. The latter is a generalization of the known one-ion solution. The properties of the homovalent solution are investigated analytically and graphically. In particular we study the phase-plane curves, which reduce to the parabolas discussed by K. S. Cole in the special case in which the current-density parameter (a linear combination of the ionic current densities) is zero.     

Stationary gene frequency distribution in the environment fluctuating between two distinct states

Summary A general method is given to obtain a stationary distribution in a stochastic one-dimensional dynamical system in which an environmental parameter specifying the dynamical system is a stationary Markov process with only two states. By applying this method, the exact stationary gene frequency distribution is obtained for a genic selection model in the environment fluctuating between two distinct states. Several limiting stationary distributions are obtained therefrom, and one of them is shown to coincide with a stationary solution of the diffusion equation heuristically derived by us for more general cases. Discussion is given on the relationship between the diffusion equations obtained by various authors starting from discrete, non-overlapping generation models.     

Theory of inbreeding and covariances between relatives under full-sib mating in diploids.

A generation matrix theory of full-sib mating is developed in which 13 mating "classes" are distinguished according to identity of genes in individuals mated and identity of genotypes as belonging to homozygous, parental, or offspring sets. The 13 times 13 matrix reveals some properties of the full-sib mating system not shown by previous work. The eigenvalues and a set of eigenvectors for the generation matrix, and the general solution for the frequencies of mating classes among descendants of an original mating of genotypes ab times cd, are given. The genotypic array of descendants in an arbitrary generation is also given. A new formula is derived for the coefficient of inbreeding in generation n + m in terms of coefficients of inbreeding in earlier generations. An algorithm is presented for calculating the probability of a given situation of identity of alleles carried by two individuals given only the indices of their own respective generations and the generation of their most recent common ancestor. The application of such probabilities to obtaining covariances between relatives in a full-sib mating system, under the assumptions of independence and non-interaction among loci, is illustrated. All results are shown to agree with previous work in special cases. All possible full sib, generation n - 1 parent-generation n + m offspring, and generation n uncle-generation n + m nephew covariances for 1 less than n + m less than or equal to 8 are obtained using the given algorithm.     

Almost periodic solution of non-autonomous Lotka-Volterra predator-prey dispersal system with delays

This paper studies a non-autonomous Lotka-Volterra almost periodic predator-prey dispersal system with discrete and continuous time delays which consists of n-patches, the prey species can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. By using comparison theorem and delay differential equation basic theory, we prove the system is uniformly persistent under some appropriate conditions. Further, by constructing suitable Lyapunov functional, we show that the system is globally asymptotically stable under some appropriate conditions. By using almost periodic functional hull theory, we show that the almost periodic system has a unique globally asymptotical stable strictly positive almost periodic solution. The conditions for the permanence, global stability of system and the existence, uniqueness of positive almost periodic solution depend on delays, so, time delays are "profitless". Finally, conclusions and two particular cases are given. These results are basically an extension of the known results for non-autonomous Lotka-Volterra systems.     

Determination of the direction and degree of an animal's tendency to migrate based on a theoretico-probabilistic analysis of its movements in a maza

Using Markov chains a mathematical model of animal displacement in the final labyrinth is obtained. Direction and value of animal tendency towards migration from a given location point are reflected in the complex of absolute frequencies of the system appearing in its states. When estimating the tendency towards migration in the applied labyrith the whole complex of frequencies can be featured by its component, e. g. by the frequencies of animal appearance in the extreme labyrinth passages.     

DeepCME: A deep learning framework for computing solution statistics of the chemical master equation

Stochastic models of biomolecular reaction networks are commonly employed in systems and synthetic biology to study the effects of stochastic fluctuations emanating from reactions involving species with low copy-numbers. For such models, the Kolmogorov’s forward equation is called the chemical master equation (CME), and it is a fundamental system of linear ordinary differential equations (ODEs) that describes the evolution of the probability distribution of the random state-vector representing the copy-numbers of all the reacting species. The size of this system is given by the number of states that are accessible by the chemical system, and for most examples of interest this number is either very large or infinite. Moreover, approximations that reduce the size of the system by retaining only a finite number of important chemical states (e.g. those with non-negligible probability) result in high-dimensional ODE systems, even when the number of reacting species is small. Consequently, accurate numerical solution of the CME is very challenging, despite the linear nature of the underlying ODEs. One often resorts to estimating the solutions via computationally intensive stochastic simulations. The goal of the present paper is to develop a novel deep-learning approach for computing solution statistics of high-dimensional CMEs by reformulating the stochastic dynamics using Kolmogorov’s backward equation. The proposed method leverages superior approximation properties of Deep Neural Networks (DNNs) to reliably estimate expectations under the CME solution for several user-defined functions of the state-vector. This method is algorithmically based on reinforcement learning and it only requires a moderate number of stochastic simulations (in comparison to typical simulation-based approaches) to train the “policy function”. This allows not just the numerical approximation of various expectations for the CME solution but also of its sensitivities with respect to all the reaction network parameters (e.g. rate constants). We provide four examples to illustrate our methodology and provide several directions for future research.     

Bioremediation of uranium-bearing wastewater: biochemical and chemical factors influencing bioprocess application

A biotechnological process for the removal of heavy metals from aqueous solution utilizes enzymatically liberated phosphate ligand which precipitates with heavy metals (M) as cell-bound MHPO(4). The enzyme, a phosphatase, obeys Michaelis-Menten kinetics in resting and immobilized cells; an integrated form of the Michaelis-Menten equation was used to calculate the apparent K(m) (K(m app.)) as operating in immobilized cells in flow-through columns by a ratio method based on the use of two enzyme loadings (E(o1), E(o2)) or two input substrate concentrations (S(o1), S(o2)). The calculated K(m app.) (4.08 mM) was substituted into an equation to describe the removal of metals by immobilized cells. In operation the activity of the bioreactor was in accordance with that predicted mathematically, within 10%. The initial tests were done at neutral pH, whereas the pH of industrial wastewaters is often low; an increase in the K(m app.) at low pH was found in previous studies. Immobilized cells were challenged with acidic mine drainage wastewaters, where the limiting factors were chemical and not biochemical. Bioreactors initially lost activity in this water, but recovered to remove uranyl ion with more than 70% efficiency under steady-state conditions in the presence of competing cations and anions. Possible reasons for the bioreactor recovery are chemical crystallization factors. (c) 1997 John Wiley & Sons, Inc.     

Different Level of Intraspecific Variation of the Bony Labyrinth Morphology in Slow- Versus Fast-Moving Primates

The vestibular system of the inner ear detects the motions of the head and is involved in maintaining balance. For this reason, this organ has been deeply studied and several scientists have tried to link its morphology with the locomotor behavior of an animal. Via high-resolution computed microtomography and geometric morphometric methods, we analyzed the intraspecific variation of the 3D morphology of the bony labyrinth (inner ear) in four species of primates differing in their locomotor adaptations: two being slow-moving taxa (Nycticebus and Perodicticus), and two being fast-moving taxa (Callithrix and Microcebus). Basically, there are very few analyses of the inter-individual variation of this organ in mammals in general, and this approach has never been attempted in primates thus far. Our results show that variation of the bony labyrinth morphology is expressed by the same ways in the different species (e.g., differences in the size, shape, and orientation of the semicircular canals, and in the width and height of the cochlea), but that slow-moving taxa exhibit a higher amount of intraspecific variation than do fast-moving taxa. Our results strengthen support for a previously published hypothesis, according to which a relaxation of the selective pressure applied to the morphology of the bony labyrinth is the likely reason for this higher amount of intraspecific variation in slow-moving taxa, and that it may be related to a reduced functional demand for rapid postural adjustments.     

Two New Books of Interest to Our Readers

The investigation is a light microscopical study of the structural development of the lamprey labyrinth, especially in Lampetra fluviatilis. Some comparisons have been made with Lampetra planeri and Petromyzon marinus. The following parts of the ear have been investigated; macula communis, its subdivision and innervation; the semicircular ducts and their ampullae; the two endolymphatic ducts and the ciliated chambers. Particular attention has been paid to the origin of these parts, the function of the ciliated chambers and the ampullae. On the basis of the present knowledge of the labyrinth an attempt has been made to see how the structural changes in it during the life cycle of the river lamprey harmonize with its way of living. Also comparative and phylogenetic aspects of the lamprey labyrinth have been made.     

传播的人群生态动力学模型

研究了HIV传播的动力学模型,描述了流行性传染病区域的人群传播规律,特别是利用摄动理论对艾滋病的传播动力学非线性方程作了定量、定性的讨论。     

A Comparative Investigation of the Bactericidal and Fungicidal Effects of Three Phenolic Disinfectants

Two methods, a capacity use-dilution test and another employing geometrical dilution, are used when comparing the bactericidal and fungicidal effects of a phenolic disinfectant containing 45% (w/w) o -phenylphenol in an aqueous soap solution of linseed oil (soap content 6·5% w/v) with the corresponding effects of the same phenolic compound in an aqueous soya oil soap solution (soap content 3·5% w/v). The soya oil soap did not change the disinfectant capacity on the different test organisms used. For the most resistant strain ( Staphylococcus aureus ) the usedilution concentration was evaluated to be slightly above 1%, i.e. 2%, which is much lower than the recommended use-dilution concentration. However, using the same method and test organisms the capacity use-dilution testing of a third phenolic disinfectant, containing p -chloro- m -cresol and o -benzyl- p -chlorophenol with a total of 9·2 (w/w) phenols in a detergent system, indicated that the recommended use-dilution concentration should be doubled.     

An immunocytochemical marker for the complex granules of tick salivary glands which traces e-granule shedding to interstitial labyrinthine spaces

An antigenic protein (12C), previously isolated from salivary glands of Rhipicephalus appendiculatus, as a possible factor in host resistance to repeated tick infestation, is labeled by protein A-gold immunocytochemistry in adult feeding ticks. It is a component of the gland's complex a-, d- and e-granules and also appears within the chitinous walls of intercalated ducts. In females, between days 4 and 7 of feeding, labeled e-granules appear also within the labyrinthine spaces of acinus type III, apparently released from e-cells as the abluminal interstitial cells initiate formation of a basolateral labyrinth. Granules thus shed are fragmented by interstitial cell processes, some fragments being phagocytized, others disintegrating to single point label scattered throughout the labyrinth. The latter possibly may pass into the acinar lumen. By the eighth day the label is gone from the labyrinth.     

On the theory of diffusion of electrolytes

In the theory of diffusion of electrolytes the following assumptions are frequently made: (i) the electrolytic solution is electrically neutral everywhere, (ii) the ionic concentrations and the electric potential all depend on a single Cartesian coordinate as the only space variable. Often the electric potential of the solution is determined on the basis of the Poisson equation alone, disregarding any other relation between this potential and the ionic concentrations. Since the Poisson equation only represents a condition which the potential fulfills, the use of this equation alone may lead to error unless the explicit relation for the potential involving a space integration of ionic concentrations is also taken into account. But if this relation is used the Poisson equation becomes redundant and, more important, assumptions (i) and (ii) appear unacceptable, the former because it leads to a zero electric potential everywhere, the latter because it is mathematically incorrect. The present paper is based on general equations of diffusion of ions, excluding the Poisson equation. These equations form a system of nonlinear integrodifferential quations whose number equals the number of ionic species present in the solution. It appears that when all ions are distributed symmetrically around a point all functions related to the above system of equations can be made dependent on a single space coordinate: the distance from the center of symmetry. Two methods of successive approximations are given for the solution of the equations in the case of spherical symmetry with limitation to the steady state. These methods are then applied to the study of the distribution of ionic concentrations and electrical potentials inside a cell of spherical shape in equilibrium with its surroundings. These methods are rapidly convergent; exact theoretical values of the electric potential are calculable on the boundary of the cell. It appears that the potential at the center of the cell is not more than ∼50% higher than at its boundary and that variation of concentration inside the cell is not very large. For instance, with 100 mV on the boundary the ionic concentration there is about four times higher than at the center. Calculations show that extremely small amounts of electricity are sufficient to account for the electric potentials currently observed. In a cell of 100 micra diameter an average concentration of only 10⁻¹⁴ mole/cm³ of a monovalent ion would be sufficient to give 1 millivolt on the boundary. This concentration is directly proportional to the voltage and inversely proportional to the square of the cell diameter. Most of the numerical results given above are obtained by considering only those ions whose electrical charge is not compensated for by ions of an opposite sign. The total concentrations may be much higher than those quoted. The theory does not take into account possible effects of structural heterogeneities which may exist in the cell, particularly of various phase boundaries. An incidental result shows that the Boltzmann distribution function in the form employed in modern theory of electrolytes is fundamentally a consequence of the mathematical theory of diffusion alone. It is pointed out, however, that Boltzmann distribution is not always compatible with the definition of the electric potential.     

Finding paths in a labyrinth based on reaction-diffusion media.

During the past few decades, many proposals were made on how to take an effective solution for finding a path in a labyrinth, one of the most well known problems of high computational complexity inherent in information processing by biomolecular and biological entities. In particular, attempts were made to use a technique attractive enough for solving this problem based on wave processes in reaction-diffusion media. Trigger waves in reaction diffusion systems spread simultaneously through all paths of the labyrinth in a highly parallel mode. Regretfully, the velocity of these waves is extremely low which gave no way for the practical implementation of this technique until now. An effective 'hardware' system was designed which was capable of finding a path in a labyrinth using fast phase waves. Three principal points were assumed as a basis for this design, i.e. (1) hybrid architecture that combined an information processing reaction-diffusion medium which performs operations of high computational complexity with a digital computer carrying out supplementary image processing operations; (2) light-sensitive information processing media of Belousov-Zhabotinsky type that enables the simulation of the labyrinth and spreading wave evolution by their images stored in the medium and reduces the problem to the image processing operations; (3) fast light-induced phase wave processes that spreads through the labyrinth in several seconds instead of hours which is typical for trigger waves inherent in reaction-diffusion media. These fundamentals along with the additional procedure of testing for labyrinth fragment connectness provided us with the opportunity to solve labyrinth problems.     

森林发展系统强解的存在唯一性及稳定性分析

对森林发展系统的动态数学模型,运用泛函分析和积分方程的理论,证明了系统强解的存在性和唯一性,并对系统的稳定性进行了讨论．