Nonlinear Analysis of the Dynamics of DNA Breathing

The base pairs that encode the genetic information in DNA show large amplitude localized excitations called DNA breathing. We discuss the experimental observations of this phenomenon and its theoretical analysis. Starting from a model introduced to study the thermal denaturation of DNA, we show that it can qualitatively describe DNA breathing but is quantitatively not satisfactory. We show how the model can be modified to be quantitatively correct. This defines a nonlinear lattice model, which is interesting in itself because it has nonlinear localized excitations, forming a new class of discrete breather.     

Formation of a hexagonal lattice structure by an R-form lipopolysaccharide of Klebsiella: effect of various divalent cations on the lattice formation

The R-form lipopolysaccharide from Klebsiella pneumoniae strain LEN-111 (O3-:K1-), from which cationic material had been removed by electrodialysis, was previously shown to form a hexagonal lattice structure with the lattice constant of 14 to 15 nm when suspended in 50 mM tris(hydroxymethyl)aminomethane buffer at pH 8.5 containing 10 mM Mg2+. Under this experimental condition, effects of other divalent metal cations on the hexagonal assembly of the electrodialyzed LPS were compared with that of Mg2+. The Zn2+, Hg2+, Cu2+, and Ni2+ could produce essentially the same hexagonal lattice structure with the lattice constant of 14.5 to 15.0 nm as that formed with Mg2+. The Cd2+, Co2+, and Fe2+ produced the hexagonal lattice structure with the lattice constant of 15.5 to 16.0 nm, and Ba2+, Sr2+, and Ca2+ produced that with the lattice constant of 18 to 19 nm. In addition, the hexagonal lattice structures formed with the latter three cations were less orderly than those formed with the other cations. When the higher concentrations of Ba2+, Sr2+, and Ca2+ were used, the lattice constants were not shortened. The length of lattice constants of the hexagonal lattice structures formed with the divalent cations did not relate to the quantity of the cations bound to the LPS. Among the divalent cations tested, Hg2+ was bound to the LPS in the smallest amount (its atomic ratio to P, 0.07), and Zn2+ and Fe2+ were bound in very large amounts (their atomic ratios to P, 2.94 and 8.28, respectively).     

Ultrasound and matter--physical interactions

The basic physical characteristics of ultrasound waves are reviewed in terms of the typical displacements, velocities, accelerations and pressures generated in various fluid media as a function of frequency. The effects on wave propagation of interfaces are considered, and the way in which waves are reflected, transmitted and mode converted at interfaces introduced. Then the nonlinear propagation of high amplitude ultrasound is explained, and its consequences, including the generation of harmonic frequencies and enhanced attenuation, considered. The absorption of ultrasonic waves and the resulting heat deposition in absorbing media are described together with factors determining the resulting temperature rises obtained. In the case of tissue these include conduction and perfusion. The characteristics of cavitation in fluid media are also briefly covered. Finally, secondary nonlinear physical effects are described. These include radiation forces on interfaces and streaming in fluids.     

耳蜗滤波器设计

提出了一种非线性耳蜗滤波器组的设计方法,设计的耳蜗滤波器组结构简单,易于实现,能模拟因输入信号电平的不同而引起的耳蜗滤波器的非线性特性,而且其特征参数能随着更新实验结果的出现灵活地加以修正。文中给出了设计细节以及具体的数字实现方法。     

Gene-culture waves of advance

Major genetic and cultural changes may have been coupled during hominid evolution. Since hominids have had a wide geographical distribution for about one million years, any mutant gene or cultural innovation that became established had to spread from its origin. A pair of nonlinear diffusion equations is derived which models the propagation of a mutant gene and a cultural innovation. Both are assumed to originate in the same locality along a linear habitat. The mutant gene and its allele are semidominant, and the two cultural choices are transmitted according to what I call the logistic attraction-repulsion model. The genes influence cultural choice, and the two interact to determine fitness. Of particular interest is the case in which mutant gene and cultural innovation are mutually dependent, neither being able to spread without the other. Each equation of the pair is similar in form to Fisher's equation, with a linear function of the other dependent variable replacing the constant coefficient in the reaction term. The partial differential equations are solved numerically to obtain the asymptotic speeds. Their form also suggests an heuristic argument which has proved useful, but I have been unable to obtain any analytic results. The waves of the system are shown to be of two types, synchronous and asynchronous. When genes and culture are mutually dependent, synchronous travelling waves can exist. However, their existence is dependent on initial conditions, and the speed of propagation is slow.     

Synoptic-scale nonlinear stationary magnetized Rossby waves in the ionospheric E-layer

Magnetized Rossby waves are produced by a dynamo electric field and represent the ionospheric generalization of tropospheric Rossby waves in a rotating atmosphere with a spatially inhomogeneous geomagnetic field. They are described by the modified Charney-Obukhov equation with a Poisson-bracket convective nonlinearity. This type of equation has solutions in the form of synoptic-scale nonlinear solitary dipole vortex structures of 1000–3000 km in diameter. With the use of equivalence conditions, various stationary nonlinear solutions are obtained and investigated analytically. The basic characteristics of stationary vortex structures for magnetized Rossby waves are investigated. Published in Russian in Fizika Plazmy, 2006, Vol. 32, No. 12, pp. 1079–1091. The text was submitted by the authors in English.     

Femtosecond IR Pump-Probe Spectroscopy of Nonlinear Energy Localization in Protein Models and Model Proteins

This paper reviews our experimental and theoretical efforts toward understanding vibrational self-trapping of the amide I and N–H mode of crystalline acetanilide (ACN), other similar hydrogen-bonded crystals, as well as of model peptides. In contrast to previous works, we used nonlinear IR spectroscopy as the experimental tool, which is specifically sensitive to the anharmonic contributions of the intramolecular interactions (as the nonlinear IR response of set of harmonic oscillators vanishes exactly). Our work reconfirms the previous assignment of the two bands of the amide I mode of ACN as being a self-trapped and a free exciton state, but in addition also establishes the lifetimes of these states and identifies the relevant phonons. Furthermore, we provide evidence for vibrationally self-trapped states also in model α-helices. However, given the short lifetime, any biological relevance in the sense of Davydov’s initial proposal can probably be ruled out.     

Dynamic and elastic properties of F-actin: a normal-modes analysis.

We examine the dynamic, elastic, and mechanical consequences of the proposed atomic models of F-actin, using a normal mode analysis. This initial analysis is done in vacuo and assumes that all monomers are rigid and equivalent. Our computation proceeds from the atomic level and, relying on a single fitting parameter, reproduces various experimental results, including persistence lengths, elastic moduli, and contact energies. The computations reveal modes of motion characteristic to all polymers, such as longitudinal pressure waves, torsional waves, and bending, as well as motions unique to F-actin. Motions typical to actin include a "groove-swinging" motion of the two long-pitch helices, as well as an axial slipping motion of the two strands. We prepare snapshots of thermally activated filaments and quantify the accumulation of azimuthal angular "disorder," variations in cross-over lengths, and various other fluctuations. We find that the orientation of a small number of select residues has a surprisingly large effect on the filament flexibility and elasticity characteristics.     

Soliton-Like Regimes and Excitation Pulse Reflection (Echo) in Homogeneous Cardiac Purkinje Fibers: Results of Numerical Simulations

On the basis of numerical simulations of the partial McAllister-Noble-Tsien equations quantitatively describing the dynamics of electrical processes in conductive cardiac Purkinje fibers we reveal unusual – soliton-like – regimes of interaction of nonlinear excitation pulses governing the heart contraction rhythm: reflection of colliding pulses instead of their annihilation. The phenomenological mechanism of the reflection effects is that in a narrow (but finite) range of the system parameters the traveling pulse presents a doublet consisting of a high-amplitude leader followed by a low-amplitude subthreshold wave. Upon collisions of pulses the leaders are annihilated, but subthreshold waves summarize becoming superthreshold and initiating two novel echo-pulses traveling in opposite directions. The phenomenon revealed presents an analogy to the effect of reflection of colliding nerve pulses, predicted recently, and can be of use in getting insight into the mechanisms of heart rhythm disturbances.     

Otoacoustic emissions from insect ears: evidence of active hearing?

Sensitive hearing organs often employ nonlinear mechanical sound processing which generates distortion-product otoacoustic emissions (DPOAE). Such emissions are also recordable from tympanal organs of insects. In vertebrates (including humans), otoacoustic emissions are considered by-products of active sound amplification through specialized sensory receptor cells in the inner ear. Force generated by these cells primarily augments the displacement amplitude of the basilar membrane and thus increases auditory sensitivity. As in vertebrates, the emissions from insect ears are based on nonlinear mechanical properties of the sense organ. Apparently, to achieve maximum sensitivity, convergent evolutionary principles have been realized in the micromechanics of these hearing organs-although vertebrates and insects possess quite different types of receptor cells in their ears. Just as in vertebrates, otoacoustic emissions from insects ears are vulnerable and depend on an intact metabolism, but so far in tympanal organs, it is not clear if auditory nonlinearity is achieved by active motility of the sensory neurons or if passive cellular characteristics cause the nonlinear behavior. In the antennal ears of flies and mosquitoes, however, active vibrations of the flagellum have been demonstrated. Our review concentrates on experiments studying the tympanal organs of grasshoppers and moths; we show that their otoacoustic emissions are produced in a frequency-specific way and can be modified by electrical stimulation of the sensory cells. Even the simple ears of notodontid moths produce distinct emissions, although they have just one auditory neuron. At present it is still uncertain, both in vertebrates and in insects, if the nonlinear amplification so essential for sensitive sound processing is primarily due to motility of the somata of specialized sensory cells or to active movement of their (stereo-)cilia. We anticipate that further experiments with the relatively simple ears of insects will help answer these questions.     

A fibril reinforced nonhomogeneous poroelastic model for articular cartilage: inhomogeneous response in unconfined compression

The depth dependence of material properties of articular cartilage, known as the zonal differences, is incorporated into a nonlinear fibril-reinforced poroelastic model developed previously in order to explore the significance of material heterogeneity in the mechanical behavior of cartilage. The material variations proposed are based on extensive observations. The collagen fibrils are modeled as a distinct constituent which reinforces the other two constituents representing proteoglycans and water. The Young's modulus and Poisson's ratio of the drained nonfibrillar matrix are so determined that the aggregate compressive modulus for confined geometry fits the experimental data. Three nonlinear factors are considered, i.e. the effect of finite deformation, the dependence of permeability on dilatation and the fibril stiffening with its tensile strain. Solutions are extracted using a finite element procedure to simulate unconfined compression tests. The features of the model are then demonstrated with an emphasis on the results obtainable only with a nonhomogeneous model, showing reasonable agreement with experiments. The model suggests mechanical behaviors significantly different from those revealed by homogeneous models: not only the depth variations of the strains which are expected by qualitative analyses, but also, for instance, the relaxation-time dependence of the axial strain which is normally not expected in a relaxation test. Therefore, such a nonhomogeneous model is necessary for better understanding of the mechanical behavior of cartilage.     

Parameterizing Spatial Models of Infectious Disease Transmission that Incorporate Infection Time Uncertainty Using Sampling-Based Likelihood Approximations

A class of discrete-time models of infectious disease spread, referred to as individual-level models (ILMs), are typically fitted in a Bayesian Markov chain Monte Carlo (MCMC) framework. These models quantify probabilistic outcomes regarding the risk of infection of susceptible individuals due to various susceptibility and transmissibility factors, including their spatial distance from infectious individuals. The infectious pressure from infected individuals exerted on susceptible individuals is intrinsic to these ILMs. Unfortunately, quantifying this infectious pressure for data sets containing many individuals can be computationally burdensome, leading to a time-consuming likelihood calculation and, thus, computationally prohibitive MCMC-based analysis. This problem worsens when using data augmentation to allow for uncertainty in infection times. In this paper, we develop sampling methods that can be used to calculate a fast, approximate likelihood when fitting such disease models. A simple random sampling approach is initially considered followed by various spatially-stratified schemes. We test and compare the performance of our methods with both simulated data and data from the 2001 foot-and-mouth disease (FMD) epidemic in the U.K. Our results indicate that substantial computation savings can be obtained—albeit, of course, with some information loss—suggesting that such techniques may be of use in the analysis of very large epidemic data sets.     

Age-dependent changes in the structure,composition and biophysical properties of a human basement membrane

Basement membranes (BMs) are considered to be uniform, approximately 100 nm-thin extracellular matrix sheets that serve as a substrate for epithelial cells, endothelial cells and myotubes. To find out whether BMs maintain their ultrastructure, protein composition and biophysical properties throughout life the natural aging history of the human inner limiting membranes (ILM) was investigated. The ILM is a BM at the vitreal surface of the retina that connects the retina with the vitreous. Transmission electron microscopy (TEM) showed that the ILM steadily increases in thickness from 70 nm at fetal stages to several microns at age 90. By the age of 20, the ILM loses its laminated structure to become an amorphous and very irregular extracellular matrix layer. Atomic force microscopy (AFM) showed that the native, hydrated ILMs are on average 4-fold thicker than the dehydrated ILMs as seen by TEM and that their thickness is prominently determined by its water-binding proteoglycans. The morphological changes are accompanied by age-related changes in the biochemical composition, whereby the relative concentrations of collagen IV and agrin increase, and the concentration of laminin decreases with age. Force-indentation measurements by AFM also showed that ILMs become increasingly stiffer with advancing age. The data suggest that BMs from other human tissues may undergo similar age-related changes.     

A Method for Analyzing Nonlinear Models When the Data are from a Split-plot or Repeated Measures Design

Statistical methods are described which can be used to compare treatments where the response model is nonlinear and the experimental design includes split-plots or repeated measures. The nonlinear analysis of covariance is described for a two-way treatment structure in a split-plot design structure, the usual split-plot experimental design. Evaluating heat tolerance in common beans as a function of temperature is used as an example to demonstrate the methodology.     

Anisotropic lattice distortions in the mollusk-made aragonite: a widespread phenomenon

In this paper, we present experimental results demonstrating systematic structural distinctions between biogenic and non-biogenic calcium carbonate. Specifically we show, by high-resolution X-ray powder diffraction on dedicated synchrotron beam lines, that the orthorhombic unit cell of the mollusk-made aragonite is anisotropically distorted as compared with that one of geological aragonite. In all investigated shells, belonging to different classes (bivalve, gastropod, and cephalopod) and taken from different habitat origins (sea, fresh water, and land), the maximum elongation of about 0.1-0.2% was found along the c-axis. The lattice distortions along the a-axis were also of the positive sign (elongation) but lower than those along the c-axis, whereas lattice distortions along the b-axis were always negative (contraction). Supporting experiments, including structural analysis after a bleach procedure, measurements of temperature-dependent lattice relaxation, measurements of the CO(2) release at elevated temperatures, signify that the observed structural distinctions are most probably caused by the organic molecules intercalating into the aragonite lattice during biomineralization. Our findings show that in some sense organisms control the atomic structure of the crystals. Deeper understanding of this phenomenon will aid in the development of new approaches to grow biomimetic composites and tailor their properties on a molecular level.     

Modulational excitation of low-frequency dust acoustic waves in the Earth’s lower ionosphere

During the observation of Perseid, Leonid, Gemenid, and Orionid meteor showers, stable low-frequency lines in the frequency range of 20–60 Hz were recorded against the radio-frequency noise background. A physical mechanism for this effect is proposed, and it is established that the effect itself is related to the modulational interaction between electromagnetic and dust acoustic waves. The dynamics of the components of a complex (dusty) ionospheric plasma with dust produced from the evolution of meteoric material is described. The conditions for the existence of dust acoustic waves in the ionosphere are considered, and the waves are shown to dissipate energy mainly in collisions of neutral particles with charged dust grains. The modulational instability of electromagnetic waves in a complex (dusty) ionospheric plasma is analyzed and is found to be driven by the nonlinear Joule heating, the ponderomotive force, and the processes governing dust charging and dynamics. The conditions for the onset of the modulational instability of electromagnetic waves, as well as its growth rate and threshold, are determined for both daytime and nighttime. It is shown that low-frequency perturbations generated in the modulational interaction are related to dust acoustic waves.     

描述神经元相互作用的非线性动力学方程的解析解

神经系统是由大量神经元构成的非线性动力系统,动力学行为十分复杂ＦＨＮ模型提供了在该系统中观察时间周期振荡这种非线性现象的实验证据．本文利用扰动法从理论上求出了ＦＨＮ模型所给出的非线性动力学方程的解析解,为进一步深入研究神经系统的动力学行为提供了理论依据     

Nonlinear control for algae growth models in the chemostat

This paper deals with output feedback control of phytoplanktonic algae growth models in the chemostat. The considered class of model is of variable yield type, meaning that the ratio between the environmental nutrient absorption rate and the cells’ growth rate varies, which is different from classical bioprocesses assumptions. On the basis of weak qualitative hypotheses on the analytical expressions of the involved biological phenomena (which guarantee robustness of the procedure toward modeling uncertainties) we propose a nonlinear controller and prove its ability to globally stabilize such processes. Finally, we illustrate our approach with numerical simulations and show its benefits for biological laboratory experiments, especially for ensuring persistence of the culture facing classical experimental problems.     

Linearized Forms of Individual-Level Models for Large-Scale Spatial Infectious Disease Systems

Individual-level models (ILMs) for infectious diseases, fitted in a Bayesian MCMC framework, are an intuitive and flexible class of models that can take into account population heterogeneity via various individual-level covariates. ILMs containing a geometric distance kernel to account for geographic heterogeneity provide a natural way to model the spatial spread of many diseases. However, in even only moderately large populations, the likelihood calculations required can be prohibitively time consuming. It is possible to speed up the computation via a technique which makes use a linearized distance kernel. Here we examine some methods of carrying out this linearization and compare the performances of these methods.     

Nonlinear modelling of renal vasoaction

The control of blood pressure is a complex mixture of neural, hormonal and intrinsic interactions at the level of the heart, kidney and blood vessels. While experimental approaches to understanding these interactions are useful, it remains difficult to conduct experiments to quantify these interactions as the number of parameters increases. Thus, modelling of such physiological systems can offer considerable assistance. Typical mathematical models which describe the ability of the blood vessels to change their diameter (vasoconstriction) assume linearity of operation. However, due to the interaction of multiple vasocontrictive and vasodilative effectors, there is a significant nonlinear response to the influence of neural factors, particularly at higher levels of nerve activity (often seen in subjects with high blood pressure) which leads to low blood flow rates. This paper proposes a number of nonlinear mathematical models for the relationship between neural influences (sympathetic nerve activity (SNA)) and renal blood flow, using a feedback path to model the predominantly nonlinear effect of local vasoactive modulators such as nitric oxide, which oppose the action of SNA. The model structures are motivated by basic physiological principles, while the model parameters are determined using numerical optimisation techniques using open-loop data collected from rabbits. The models were verified by demonstrating correlation between experimental results and model outputs.