Impact of receptor-ligand distance on adhesion cluster stability

Cells in multicellular organisms adhere to the extracellular matrix through two-dimensional clusters spanning a size range from very few to thousands of adhesion bonds. For many common receptor-ligand systems, the ligands are tethered to a surface via polymeric spacers with finite binding range, thus adhesion cluster stability crucially depends on receptor-ligand distance. We introduce a one-step master equation which incorporates the effect of cooperative binding through a finite number of polymeric ligand tethers. We also derive Fokker-Planck and mean field equations as continuum limits of the master equation. Polymers are modeled either as harmonic springs or as worm-like chains. In both cases, we find bistability between bound and unbound states for intermediate values of receptor-ligand distance and calculate the corresponding switching times. For small cluster sizes, stochastic effects destabilize the clusters at large separation, as shown by a detailed analysis of the stochastic potential resulting from the Fokker-Planck equation.     

有三重态的四能级系统的光学双稳态

对一种有着单重态和三重态的典型的有机物的四能级系统的光学双稳进行了研究。由密度矩阵的速率方程近拟推导出了光学双稳的状态方程。对单重态和三重态吸收或色散情况下的双稳情况用数值解的方法进行了讨论。文中分析了单重态和三重态的合作参数、原子失谐参数和腔失谐参数对双稳的影响。     

Additive noise in noise-induced nonequilibrium transitions

We study different nonlinear systems which possess noise-induced nonequlibrium transitions and shed light on the role of additive noise in these effects. We find that the influence of additive noise can be very nontrivial: it can induce first- and second-order phase transitions, can change properties of on-off intermittency, or stabilize oscillations. For the Swift-Hohenberg coupling, that is a paradigm in the study of pattern formation, we show that additive noise can cause the formation of ordered spatial patterns in distributed systems. We show also the effect of doubly stochastic resonance, which differs from stochastic resonance, because the influence of noise is twofold: multiplicative noise and coupling induce a bistability of a system, and additive noise changes a response of this noise-induced structure to the periodic driving. Despite the close similarity, we point out several important distinctions between conventional stochastic resonance and doubly stochastic resonance. Finally, we discuss open questions and possible experimental implementations. (c) 2001 American Institute of Physics.     

Cellular Biology in Terms of Stochastic Nonlinear Biochemical Dynamics: Emergent Properties,Isogenetic Variations and Chemical System Inheritability

Based on a stochastic, nonlinear, open biochemical reaction system perspective, we present an analytical theory for cellular biochemical processes. The chemical master equation (CME) approach provides a unifying mathematical framework for cellular modeling. We apply this theory to both self-regulating gene networks and phosphorylation-dephosphorylation signaling modules with feedbacks. Two types of bistability are illustrated in mesoscopic biochemical systems: one that has a macroscopic, deterministic counterpart and another that does not. In certain cases, the latter stochastic bistability is shown to be a “ghost” of the extinction phenomenon. We argue the thermal fluctuations inherent in molecular processes do not disappear in mesoscopic cell-sized nonlinear systems; rather they manifest themselves as isogenetic variations on a different time scale. Isogenetic biochemical variations in terms of the stochastic attractors can have extremely long lifetime. Transitions among discrete stochastic attractors spend most of the time in “waiting”, exhibit punctuated equilibria. It can be naturally passed to “daughter cells” via a simple growth and division process. The CME system follows a set of nonequilibrium thermodynamic laws that include non-increasing free energy F(t) with external energy drive Q _hk ≥0, and total entropy production rate e _p =−dF/dt+Q _hk ≥0. In the thermodynamic limit, with a system’s size being infinitely large, the nonlinear bistability in the CME exhibits many of the characteristics of macroscopic equilibrium phase transition.     

The nature of bursting noises,stochastic resonance and deterministic chaos in excitable neurons

We study the Hindmarsh-Rose model of excitable neurons and show that in the asymptotic limit this monostable model can possess some kind of dynamical bistability: small-amplitude quasiharmonic and large-amplitude relaxational oscillations can be simultaneously excited and their formation is accompanied by a narrow hysteresis. We show that bursting noises, stochastic resonance and deterministic chaos are determined by random transitions between these two dynamical states under slow and small changes of one of the model variables (z). We find that these effects take place even for such model parameters when hysteresis transforms into a step and they disappear when this step is smoothed out enough. We analyze some characteristics and conditions of formation of the deterministic chaos. We emphasize that such dynamical bistability and the effects related to it are universal phenomena and occur in a wide class of dynamical systems of different nature including brusselator.     

Tunable all-optical bistability in a semiconductor quantum dot damped by a phase-dependent reservoir

We propose a method of frequency and phase control of optical bistability in a unidirectional ring cavity containing a semiconductor structure which is characterized as a ladder three-level system. The system interacts with a coherent probe field, and a control field which consists of a strong coherent field and a weak amplitude-fluctuating stochastic field. A perturbative solution of the master equation of the system allows to eliminate the stochastic field and provides a physical picture in terms of correlation properties of the stochastic field. We find that the bistable response can be modified strongly by means of the amplitude, the frequency and the phase of the stochastic field. In order to illustrate the feasibility of the results, we use parameter values corresponding to an semiconductor quantum dot (QD). This investigation may be used to optimize and control the optical switching process in the QD solid-state system, which is much more practical than that in atomic systems.     

Hysteresis and memory of the magnetic resonance of conduction electrons in solids. From bistability to stochastic resonance

The magnetic resonance line of conduction electrons in solids may exhibit bistable hysteresis if several conditions are fulfilled. Its mechanism is presented and the manifestation of bistability in the ESR of conduction electrons in single crystal and polycrystalline samples is discussed. The characteristics of the dynamics of the bistability show that bistable resonance can be assimilated to one-dimensional overdamped motion of the spin system in the nuclear field space, driven by a bistable potential. It is shown for the first time that noise acting on this bistable resonance can create order, by the phenomenon of stochastic resonance.     

Stochastic resonance between the limiting cycles of precession dynamics

A new type of stochastic resonance that arises between two precession modes under dynamic bistability conditions and is excited by an alternating magnetic field, including a harmonic signal and a white noise, has been studied using a numerical analysis of the uniform magnetization precession in a thin film. The spectrum of the steady-state dynamics of the system at stochastic resonance has been investigated, and its distinctive features have been revealed for the longitudinal and transverse orientations of the additional alternating field.     

Optical Bistability in Three-Component Solutions of Complex Molecules

The possibility of realizing internal optical bistability in solutions of complex polar molecules in binary solvents is theoretically investigated. The hysteresis dependences of absorption on the exciting-radiation intensity for these solutions are shown to be related to the cooperative nature of the process of nonspecific solvation.     

Deterministic chaos and noise in optical bistability

The time-dependent solutions of the mean-field Maxwell-Bloch equations for optical bistability are studied numerically for the deterministic equations and the stochastic equations with additional noise sources. From the solutions of the deterministic equations, a discrete map is constructed showing that the periodic and chaotic solutions form a Feigenbaum scenarium. Inclusion of noise sources leads to a finite lifetime of the states in the upper bistable branch and to destabilization of higher periodic solutions.     

Evidence of stochastic resonance in a laser with saturable absorber: Experiment and theory

A laser with intracavity saturable absorber showing optical bistability is investigated through the simultaneous injection of modulation and noise on the pumping parameter; stochastic resonance is exhibited in the measured signal-to-noise ratio of the laser intensity.     

Optical bistability by two laser beams in photorefractive crystals

For a nonlinear medium, a given incident laser beam may produce different transmitted light waves. This phenomenon (the so-called optical bistability) corresponds to multiple solutions of the boundary value problems of the nonlinear Helmholtz equation. Optical bistability can be useful in the design of optical switches. Devices that display this behavior could potentially play a major role in the development of optical communication systems and computing. In this article we present experimental results concerning the optical bistability in photorefractive BaTiO₃:Fe crystal. Two laser beams were used to interact with the photorefractive crystal which resulted in the bistability of the intensity of transmitted wave. This was achieved without the application of any optical resonator. High contrast optical bistability is found experimentally in the pump-ratio dependence of the output intensity.     

Tubulin bistability and polymorphic dynamics of microtubules

Based on the hypothesis that the GDP-tubulin dimer is a conformationally bistable molecule-rapidly fluctuating between a discrete curved and a straight state-we develop a model for polymorphic dynamics of the microtubule lattice. We show that GDP-tubulin bistability consistently explains unusual dynamic fluctuations, the apparent length-stiffness relation of grafted taxol-stabilized microtubules, and the curved-helical appearance of microtubules in general. When clamped by one end the microtubules undergo an unusual zero energy motion-in its effect reminiscent of a limited rotational hinge. We conclude that microtubules exist in highly cooperative energy-degenerate helical states and discuss possible implications in vivo.     

Optical bistability in defective photonic multilayers doped by graphene

We study the optical bistability (OB) in photonic multilayers doped by graphene sheets, stacking two Bragg reflectors with a defect layer between the reflectors. OB stems from the nonlinear effect of graphene, so the local field of defect mode (DM) could enhance the nonlinearity and reduce the thresholds of bistability. The structure achieves the tunability of bistability due to that the DM frequency and transmittance could be modulated by the chemical potential. Bistability thresholds and interval of the two stable states could be remarkably reduced by decreasing the chemical potential. A lager Bragg periodic number could increase the localizing of field, but the graphene loss may decrease the intensity of transmission light. We have concluded an appropriate periodic number to achieve OB. The study suggests that the tunable bistability of the structure could be used for all-optical switches in optical communication systems.     

Tristable and multiple bistable activity in complex random binary networks of two-state units

We study complex networks of stochastic two-state units. Our aim is to model discrete stochastic excitable dynamics with a rest and an excited state. Both states are assumed to possess different waiting time distributions. The rest state is treated as an activation process with an exponentially distributed life time, whereas the latter in the excited state shall have a constant mean which may originate from any distribution. The activation rate of any single unit is determined by its neighbors according to a random complex network structure. In order to treat this problem in an analytical way, we use a heterogeneous mean-field approximation yielding a set of equations generally valid for uncorrelated random networks. Based on this derivation we focus on random binary networks where the network is solely comprised of nodes with either of two degrees. The ratio between the two degrees is shown to be a crucial parameter. Dependent on the composition of the network the steady states show the usual transition from disorder to homogeneously ordered bistability as well as new scenarios that include inhomogeneous ordered and disordered bistability as well as tristability. The various steady states differ in their spiking activity expressed by a state dependent spiking rate. Numerical simulations agree with analytic results of the heterogeneous mean-field approximation.     

物理系统的稳定性与双稳现象(Ⅰ)

以力学系统（非线性振动），热力学系统（气液相变与铁磁相变）及光学系统中的几种双稳现象为实例，采用初等方法阐明系统的稳定性与双稳的基本原理。     

Laser-driven blackbody radiator with bistability

We report a particular construction of a laser-driven blackbody radiator with bistability mode based on efficient light-into-heat conversion of a rare earth system. The laser-induced thermal avalanche nonlinearity and the internal stimulative feedback mechanisms are revealed to interpret the typical S-pattern bistability. The standard blackbody radiation and the sizable bistability mode are experimentally demonstrated through ultrabroadband thermal spectra measurements of ZrO₂:Yb–Tm nanophase compounds. Such a noncontact, laser-driven scheme for microscale blackbody radiation has attractive applications for compact standard spectra source and broadband spectra switching in the on-chip all-optical systems.     

光学耗散系统的准热力学模型及其在光学双稳性相变问题上的应用

本文以光学耗散系统为范例,论证在满足细致平衡原理的条件下,可以与传统热力学相平行地发展一种“准热力学”模型。然后运用此模型系统而普遍地讨论了光学双稳系统的临界现象与相变。又借助Ginzburg-Landau模型处理了光学双稳性(第二类)临界点附近的涨落与关联。将平衡热力学的Landau相变理论推广到具有双稳性并远离热平衡的耗散系统。     

色散对单模激光系统非线性效应的影响

研究在强光场的作用下 ,激光系统中的腔内介质的折射率不再是常数而引起的非线性效应 ,即色散型激光系统的动力学行为。研究结果表明 ,这类系统的输出场会呈现双稳态 ,并利用极值法确定了描述这类色散型激光系统的Maxvell- bloch方程是现双稳态的参数临界点和双稳态区域     

非锁相Lorenz-Haken方程动力学研究

考虑原子的相干性和经典注入光场，利用随机微分方程给出非锁相条件下的Lorenz-Haken方程，研究失谐量、注入经典光场和原子相干性对非锁相Lorenz-Haken方程动力学特性的影响．在激光运转情形，失谐量造成光场位相的混沌，系统在不同条件下，出现四吸引子、双吸引子及单吸引子混沌状态，且体系的分数维维数较锁相条件下增加．光场失谐量、注入光场和原子相干性可抑制混沌．在双稳态运转下，光场位相为π的偶数倍或奇数倍，使光场稳定于正值和负值，故体系出现对称双稳态对，但无混沌状态． 关键词： 非锁相Lorenz-Haken方程 混沌 原子相干性 注入光场