Pacer cell response to periodic Zeitgebers

Almost all organisms show some kind of time periodicity in their behavior. In mammals, the neurons of the suprachiasmatic nucleus form a biological clock regulating the activity-inactivity cycle of the animal. The main question is how this clock is able to entrain to the natural 24 h light-dark cycle by which it is stimulated. Such a system is usually modeled as a collection of mutually coupled two-state (active-inactive) phase oscillators with an external stimulus (Zeitgeber). In this article however, we investigate the entrainment of a single pacer cell to the ensemble of other pacer cells. Moreover the stimulus of the ensemble is taken to be periodic. The pacer cell interacts with its environment by phase delay at the end of its activity interval and phase advance at the end of its inactivity interval. We develop a mathematical model for this system, naturally leading to a circle map depending on parameters like the intrinsic period and phase delay and advance. The existence of resonance tongues in a circle map shows that an individual pacer cell is able to synchronize with the ensemble. We furthermore show how the parameters in the model can be related to biological observable quantities. Finally we give several directions of further research.     

A new association state of solutes in nanoconfined aqueous solutions

Recently, we have found a reversible transition between the dispersion and aggregation states of solute molecules in aqueous solutions confined in nanoscale geometry, where solutes exhibit distinct behavior in a new association state from that in the dispersion and aggregation states observed usually in macroscopic systems. However, it remains unknown whether this new association state of solute molecules found in nanoconfined systems would vanish with the system size increasing and approaching the macroscopic scale. Here, we achieve the phase diagram of solute association states by making the analyses of Gibbs free energy of solutes in nanoconfined aqueous solutions in detail. In the phase diagram, we observe a closed regime with a finite system size of nanoconfined aqueous solutions and a solute concentration range, only in which there exists the new association state of solutes with the reversible transition between the aggregation and dispersion states, and there indeed exists an upper limit of the system size for the new association state, around several tens nanometers. These findings regarding the intimate connection between the system size and the solute association behavior provides the comprehensive understanding of the association dynamics of solutes in nanoconfined environment.     

计算相位响应曲线的方波扰动直接算法

通过相位响应曲线可对具有极限环周期运动的动力系统的性质有更为深入的理解.神经元是一个典型的动力系统,因此相位响应曲线提供了一种研究神经元重复周期放电行为的新思路.本文提出一种求解相位响应曲线的方法,即方波扰动的直接算法,通过Hodgkin-Huxley,Fitz Hugh-Nagumo,Morris-Lecar和Hindmarsh-Rose神经元模型验证该算法可计算周期峰放电、周期簇放电的相位响应曲线.该算法克服了其他算法在运用过程中的局限性.利用该算法计算结果表明:周期峰放电的相位响应曲线类型是由其分岔类型所决定;在Morris-Lecar模型中发现一种开始于Hopf分岔终止于鞍点同宿轨道分岔的阈上周期振荡,其相位响应曲线属于第二类型.通过大量的相位响应曲线的计算发现相位响应的相对大小及正负性仅取决于扰动所施加的时间,而且周期簇放电的相位响应曲线比周期峰放电的相位响应曲线更为复杂.     

电流变液中悬浮粒子的布朗运动与其聚集之间关系

在外电场作用下,电流变液中粒子链的聚集与其布朗运动密切相关。为了具体分析这种关系,采用不分离但有相互运动的双球构成的系统去简化粒子链。通过分析双球系统布朗运动特性,得到其无规运动轨迹维数小于2,大量这样的系统在平面中就不可能均匀分布。这说明由于存在布朗运动,在外电场中电流变液中粒子链必然相互聚集,即形成高密度区与低密度区。 关键词：     

Dynamic Scaling of Lipofuscin Deposition in Aging Cells

Lipofuscin is a membrane-bound cellular waste that can be neither degraded nor ejected from the cell but can only be diluted through cell division and subsequent growth. The fate of postmitotic (non-dividing) cells such as neurons, cardiac myocytes, skeletal muscle fibers, and retinal pigment epithelial cells (RPE) is to accumulate lipofuscin, which as an “aging pigment” has been considered a reliable biomarker for the age of cells. Environmental stress can accelerate the accumulation of lipofuscin. For example, accumulation in brain cells appears to be an important issue connected with heavy consumption of alcohol. Lipofuscin is made of free-radical-damaged protein and fat, whose abnormal accumulation is related to a range of disorders including Type IV mucolipidosis (ML4), Amyotrophic Lateral Sclerosis (ALS), Alzheimer’s disease, Parkinson disease, and age-related macular degeneration (AMD) which is the leading cause of blindness beyond the age of 50 years. The study of lipofuscin formation and growth is important, because of their association with cellular aging. We introduce a model of non-equilibrium cluster growth and aggregation that we have developed for studying the formation and growth of lipofuscin. As an example of lipofuscin deposit in a given kind of postmitotic cell, we study the kinetics of lipofuscin growth in a RPE cell. Our results agree with a linear growth of the number of lipofuscin granules with age. We apply the dynamic scaling approach to our model and find excellent data collapse for the cluster size distribution. An unusual feature of our model is that while small particles are removed from the cell the larger ones become fixed and grow by aggregation.     

Phase resetting effects for robust cycles between chaotic sets

In the presence of symmetries or invariant subspaces, attractors in dynamical systems can become very complicated, owing to the interaction with the invariant subspaces. This gives rise to a number of new phenomena, including that of robust attractors showing chaotic itinerancy. At the simplest level this is an attracting heteroclinic cycle between equilibria, but cycles between more general invariant sets are also possible. In this paper we introduce and discuss an instructive example of an ordinary differential equation where one can observe and analyze robust cycling behavior. By design, we can show that there is a robust cycle between invariant sets that may be chaotic saddles (whose internal dynamics correspond to a R?ssler system), and/or saddle equilibria. For this model, we distinguish between cycling that includes phase resetting connections (where there is only one connecting trajectory) and more general non(phase) resetting cases, where there may be an infinite number (even a continuum) of connections. In the nonresetting case there is a question of connection selection: which connections are observed for typical attracted trajectories? We discuss the instability of this cycling to resonances of Lyapunov exponents and relate this to a conjecture that phase resetting cycles typically lead to stable periodic orbits at instability, whereas more general cases may give rise to "stuck on" cycling. Finally, we discuss how the presence of positive Lyapunov exponents of the chaotic saddle mean that we need to be very careful in interpreting numerical simulations where the return times become long; this can critically influence the simulation of phase resetting and connection selection.     

Autonomous coupled oscillators with hyperbolic strange attractors

We propose several examples of smooth low-order autonomous dynamical systems which have apparently uniformly hyperbolic attractors. The general idea is based on the use of coupled self-sustained oscillators where, due to certain amplitude nonlinearities, successive epochs of damped and excited oscillations alternate. Because of additional, phase sensitive coupling terms in the equations, the transfer of excitation from one oscillator to another is accompanied by a phase transformation corresponding to some chaotic map (in particular, an expanding circle map or Anosov map of a torus). The first example we construct is a minimal model possessing an attractor of the Smale-Williams type. It is a four-dimensional system composed of two oscillators. The underlying amplitude equations are similar to those of the predator-pray model. The other three examples are systems of three coupled oscillators with a heteroclinic cycle. This scheme presents more variability for the phase manipulations: in the six-dimensional system not only the Smale-Williams attractor, but also an attractor with Arnold cat map dynamics near a two-dimensional toral surface, and a hyperchaotic attractor with two positive Lyapunov exponents, are realized.     

Non-smooth bursting analysis of a Filippov-type system with multiple-frequency excitations

The main purpose of this paper is to explore the patterns of the bursting oscillations and the non-smooth dynamical behaviours in a Filippov-type system which possesses parametric and external periodic excitations. We take a coupled system consisting of Duffing and Van der Pol oscillators as an example. Owing to the existence of an order gap between the exciting frequency and the natural one, we can regard a single periodic excitation as a slow-varying parameter, and the other periodic excitations can be transformed as functions of the slow-varying parameter when the exciting frequency is far less than the natural one. By analysing the subsystems, we derive equilibrium branches and related bifurcations with the variation of the slow-varying parameter. Even though the equilibrium branches with two different frequencies of the parametric excitation have a similar structure, the tortuousness of the equilibrium branches is diverse, and the number of extreme points is changed from 6 to 10. Overlying the equilibrium branches with the transformed phase portrait and employing the evolutionary process of the limit cycle induced by the Hopf bifurcation, the critical conditions of the homoclinic bifurcation and multisliding bifurcation are derived. Numerical simulation verifies the results well.     

Aggregation methods in dynamical systems and applications in population and community dynamics

Approximate aggregation techniques allow one to transform a complex system involving many coupled variables into a simpler reduced model with a lesser number of global variables in such a way that the dynamics of the former can be approximated by that of the latter. In ecology, as a paradigmatic example, we are faced with modelling complex systems involving many variables corresponding to various interacting organization levels. This review is devoted to approximate aggregation methods that are based on the existence of different time scales, which is the case in many real systems as ecological ones where the different organization levels (individual, population, community and ecosystem) possess a different characteristic time scale. Two main goals of variables aggregation are dealt with in this work. The first one is to reduce the dimension of the mathematical model to be handled analytically and the second one is to understand how different organization levels interact and which properties of a given level emerge at other levels. The review is organized in three sections devoted to aggregation methods associated to different mathematical formalisms: ordinary differential equations, infinite-dimensional evolution equations and difference equations.     

Network Aggregation Process in Multilayer Air Transportation Networks

The air transportation network,one of the common multilayer complex systems,is composed of a collection of individual airlines,and each airline corresponds to a different layer.An important question is then how many airlines are really necessary to represent the optimal structure of a multilayer air transportation system.Here we take the Chinese air transportation network(CATN) as an example to explore the nature of multiplex systems through the procedure of network aggregation.Specifically,we propose a series of structural measures to characterize the CATN from the multilayered to the aggregated network level.We show how these measures evolve during the network aggregation process in which layers are gradually merged together and find that there is an evident structural transition that happened in the aggregated network with nine randomly chosen airlines merged,where the network features and construction cost of this network are almost equivalent to those of the present CATN with twenty-two airlines under this condition.These findings could shed some light on network structure optimization and management of the Chinese air transportation system.     

A unified symmetry of nonholonomic mechanical systems in phase space

In this paper, we have studied the unified symmetry of a nonholonomic mechanical system in phase space. The definition and the criterion of a unified symmetry of the nonholonomic mechanical system in phase space are given under general infinitesimal transformations of groups in which time is variable. The Noether conserved quantity, the generalized Hojman conserved quantity and the Mei conserved quantity are obtained from the unified symmetry. An example is given to illustrate the application of the results.     

Model for folding and aggregation in RNA secondary structures

We study the statistical mechanics of RNA secondary structures designed to have an attraction between two different types of structures as a model system for heteropolymer aggregation. The competition between the branching entropy of the secondary structure and the energy gained by pairing drives the RNA to undergo a "temperature independent" second order phase transition from a molten to an aggregated phase. The aggregated phase thus obtained has a macroscopically large number of contacts between different RNAs. The partition function scaling exponent for this phase is theta approximately 1/2 and the crossover exponent of the phase transition is nu approximately 5/3. The relevance of these calculations to the aggregation of biological molecules is discussed.     

Phase transitions in simple models of rod-like and disc-like micelles

The interplay of interactions between micelles, and the aggregation of these micelles into large, highly anisotropic micelles, is studied. Simple, hard-body, models of rod-like and disc-like micelles are used, which allows us to apply fundamental measure theory to determine the free energy. Then we study the phase transition from the fluid phase to a liquid crystalline phase. We find that aggregation induces a strongly first order transition from a fluid phase of small micelles to a close packed liquid crystalline phase of infinitely large micelles. Received: 3 December 1997     

Different effects of redundant feedback loops on a bistable switch

Bistable switches have important roles in cellular decision-making processes. Bistability can be the consequence of positive or double-negative feedback loops. Although necessary, such feedback is not sufficient for bistability, which also requires nonlinearity. Nonlinearity can be provided by synergy of multiple feedback loops or by an ultrasensitive response within a single feedback loop. However, these two possibilities are not mutually exclusive; a combination of them is also possible. Here we analyze a biochemical regulatory network that controls a crucial cell cycle transition in all eukaryotic cells and contains multiple redundant feedback loops and nonlinearity. We show in this realistic biological example that two redundant feedback loops have different effects on the position of one of the saddle-node bifurcations of the system, which determines where the system switches. This illustrates that even though the roles of positive and double-negative feedbacks have been regarded as equivalent, the difference in their architectures can lead to differences in their effects on the system. We speculate that this conclusion could be general for other bistable systems with redundant feedback loops.     

Direct transition from a stable equilibrium to quasiperiodicity in non-smooth systems

The purpose of this Letter is to show how a border-collision bifurcation in a piecewise-smooth dynamical system can produce a direct transition from a stable equilibrium point to a two-dimensional invariant torus. Considering a system of nonautonomous differential equations describing the behavior of a power electronic DC/DC converter, we first determine the chart of dynamical modes and show that there is a region of parameter space in which the system has a single stable equilibrium point. Under variation of the parameters, this equilibrium may collide with a discontinuity boundary between two smooth regions in phase space. When this happens, one can observe a number of different bifurcation scenarios. One scenario is the continuous transformation of the stable equilibrium into a stable period-1 cycle. Another is the transformation of the stable equilibrium into an unstable period-1 cycle with complex conjugate multipliers, and the associated formation of a two-dimensional (ergodic or resonant) torus.     

机械传动空回对伺服性能的影响分析

机械传动空回主要由传动系统间隙、传动链弹性变形以及机械构件受载变形等因素产生,对伺服系统的控制精度和稳定性等具有较大影响。分析了机械传动空回的数学模型,建立了考虑传动空回的伺服系统框图,并通过典型仿真实例,深入分析机械传动空回建模及其对伺服性能的影响。分析结果表明, 传动空回对伺服性能的影响主要体现在2个方面:一是引起相位滞后,影响系统的稳定性;二是引起极限环振荡,产生自振静态误差。     

A composite high-pressure cell with sintered diamond insets for study of thermoelectric and thermomagnetic properties in a range up to 30 GPa: Application to Pr and PbTe

A composite high-pressure cell with the sintered diamond insets is reported to be an effective tool for investigation of transport properties of solids under pressure as high as ∼30 GPa. The temperature distribution inside the cell was calculated. Using this cell, the pressure-driven phase transitions in praseodymium (Pr) have been studied by the thermopower technique (Seebeck effect). The results have shown that a scenario of the phase transitions in Pr (existence of the monoclinic C2/m phase) crucially depends on defects and distortions in a crystal lattice. So, the monoclinic phase was noticeable only for the first pressurization cycle. A technique of measurement of the longitudinal and the transverse thermomagnetic Nernst-Ettingshausen (N-E) effects (magnetothermopower) under high P is explained. With an example of lead telluride (PbTe), it is demonstrated that magnetic field can significantly improve the thermoelectric efficiency under pressure. The merits of the cell developed are discussed concerning basic research and technologies.