系统规模对群体行为的效果

影响细胞群体行为的因素是多种多样的, 除了以前研究的细胞通讯方式和环境因素外, 还与现有文献没有或很少研究的细胞数目(即系统规模)有关. 本文研究了系统规模对一类合成多细胞通讯系统的聚类行为的影响. 在该系统中, 单个系统是由压制振动子和基于延迟的松弛振子整合而成的振子, 而振子之间通过群体感应机制相互耦合. 通过分岔分析和数值模拟发现: 细胞数目的增加不仅可以改变平衡态聚类稳定性区间的大小并诱导新的聚类行为, 而且有利于扩大平衡态聚类的吸引域, 表明细胞分化可能与系统规模有密切关系; 细胞数目的增加还可以极大地丰富平衡态聚类和振动聚类的表现形式和共存方式, 为生物体对环境的适应性提供了良好的基础. 我们的结果不仅扩充了耦合系统的动力学行为, 也为理解多细胞现象奠定了基础. 关键词： 系统规模 群体感应 群体行为 耦合振子     

Suppression of chaos and other dynamical transitions induced by intercellular coupling in a model for cyclic AMP signaling in Dictyostelium cells

The effect of intercellular coupling on the switching between periodic behavior and chaos is investigated in a model for cAMP oscillations in Dictyostelium cells. We first analyze the dynamic behavior of a homogeneous cell population which is governed by a three-variable differential system for which bifurcation diagrams are obtained as a function of two control parameters. We then consider the mixing of two populations behaving in a chaotic and periodic manner, respectively. Cells are coupled through the sharing of a common chemical intermediate, extracellular cAMP, which controls its production and release by the cells into the extracellular medium; the dynamics of the mixed suspension is governed by a five-variable differential system. When the two cell populations differ by the value of a single parameter which measures the activity of the enzyme that degrades extracellular cAMP, the bifurcation diagram established for the three-variable homogeneous population can be used to predict the dynamic behavior of the mixed suspension. The analysis shows that a small proportion of periodic cells can suppress chaos in the mixed suspension. Such a fragility of chaos originates from the relative smallness of the domain of aperiodic oscillations in parameter space. The bifurcation diagram is used to obtain the minimum fraction of periodic cells suppressing chaos. These results are related to the suppression of chaos by the small-amplitude periodic forcing of a strange attractor. Numerical simulations further show how the coupling of periodic cells with chaotic cells can produce chaos, bursting, simple periodic oscillations, or a stable steady state; the coupling between two populations at steady state can produce similar modes of dynamic behavior.     

Controlling dynamical behavior of drive-response system through linear augmentation

Unidirectionally coupled chaotic systems give rise to driver induced bistability in response system under certain parameters setting. Such a system is studied here with augmented dynamics. A linear augmentation provides a controlled dynamical behavior of response system in two different ways: augmented drive system brings the stabilization of the steady state where as augmented response system is able to control the bistability. We present a detailed analysis of Lorenz–Rössler system with linear augmentation for controlled dynamical behavior.     

From excitability to oscillations: A case study in vasomotion

One consequence of cell-to-cell communication is the appearance of synchronized behavior, where many cells cooperate to generate new dynamical patterns. We present a simple functional model of vasomotion based on the concept of a two-mode oscillator with dual interactions: via relatively slow diffusive coupling that gives rise to wave dynamics and via fast changes in membrane potential that propagate almost instantly over significant distances. The model reproduces the basic calcium dynamics of the vascular smooth muscle cell: calcium waves which upon increased activity of cGMP-sensitive calcium-dependent chloride channels in the plasma membrane may synchronize into whole-cell oscillations which subsequently may spread across a large population of cells. We show how heterogeneity of the system can induce new patterns.     

Selective effects of noise by stochastic multi-resonance in coupled cells system

By investigating a stochastic model for intracellular calcium oscillations proposed by Höfer, we have analyzed the transmission behavior of calcium signaling in a one-dimensional two-way coupled hepatocytes system. It is shown that when the first cell is subjected to the external noise, the output signal-to-noise ratio (SNR) in the cell exhibits two maxima as a function of external noise intensity, indicating the occurrence of stochastic bi-resonance (SBR). It is more important that when cells are coupled together, the resonant behavior in the 1st cell propagates along the chain with different features through the coupling effect. The cells whose locations are comparatively close to or far from the 1st cell can show SBR, while the cells located in the middle position can display stochastic multi-resonance (SMR). Furthermore, the number of cells that can show SMR increases with coupling strength enhancing. These results indicate that the cells system may make an effective choice in response to external signaling induced by noise, through the mechanism of SMR by adjusting coupling strength.     

Regular and Chaotic Spatiotemporal Patterns in a Model of Slime Mold Aggregation

In this paper we proposed a spatial modulated two-variable Martiel-Goldbeter model to describe the complex spatiotemporal disorder dynamical behavior during development of Dictyostelium discoideum strain FR17. As the nonlinear modulated parameter A and diffusion coefficient E varied, the system shows: 1) multiperiodic phase, 2) co-existence phase of chaotic and multi-periodic state, 3) spatiotemporal chaotic phase, 4) co-existence phase of chaotic, multi-periodic and steady state, and 5) co-existence phase of chaotic and steady state. These phases can be described by spatiotemporal power spectra, pattern distribution function and Lyapunov spectra. We believed that the complex spatiotemporal disorder dynamical behavior during development of Dictyosteliurn discoideum strain FR17 is a spatiotemporal chaotic state.     

Numerical bifurcation analysis of two coupled FitzHugh-Nagumo oscillators

The behavior of neurons can be modeled by the FitzHugh-Nagumo oscillator model, consisting of two nonlinear differential equations, which simulates the behavior of nerve impulse conduction through the neuronal membrane. In this work, we numerically study the dynamical behavior of two coupled FitzHugh-Nagumo oscillators. We consider unidirectional and bidirectional couplings, for which Lyapunov and isoperiodic diagrams were constructed calculating the Lyapunov exponents and the number of the local maxima of a variable in one period interval of the time-series, respectively. By numerical continuation method the bifurcation curves are also obtained for both couplings. The dynamics of the networks here investigated are presented in terms of the variation between the coupling strength of the oscillators and other parameters of the system. For the network of two oscillators unidirectionally coupled, the results show the existence of Arnold tongues, self-organized sequentially in a branch of a Stern-Brocot tree and by the bifurcation curves it became evident the connection between these Arnold tongues with other periodic structures in Lyapunov diagrams. That system also presents multistability shown in the planes of the basin of attractions.     

Dynamics of nonequilibrium membrane bud formation

The dynamical response of a lipid membrane to a local perturbation of its molecular symmetry is investigated theoretically. A density asymmetry between the two membrane leaflets is predominantly released by in-plane lipid diffusion or membrane curvature, depending upon the spatial extent of the perturbation. It may result in the formation of nonequilibrium structures (buds), for which a dynamical size selection is observed. A preferred size in the microm range is predicted, as a signature of the crossover between membrane and solvent dominated dynamical membrane response.     

物理学在肿瘤细胞的极性及迁移研究中的应用

肿瘤细胞和所处微环境的物理性质, 以及它们之间的相互物理作用对于肿瘤的产生、发展与转移都有极大的影响, 这使得从物理学角度探索肿瘤研究成为了必然趋势. 肿瘤转移是癌症致死的最大因素, 而肿瘤细胞迁移中的极化是肿瘤转移的重要一步. 本文总结了物理学实验和模型在揭示细胞迁移和极化机理方面的贡献. 实验上应用最新的微流控芯片技术与表面微模型化技术等手段, 研究空间维度、黏附行为、机械力等物理信号对于细胞极性的建立与保持以及细胞迁移行为的影响后, 发现物理信号与生化反应之间的相互耦合对于细胞迁移有着至关重要的作用; 理论上基于扩散反应方程, 已经建立了一系列表征细胞极化的模型. 今后的研究将结合物理实验建立肿瘤细胞迁移中的极化模型, 进而发展针对肿瘤细胞感知物理信号的新的治疗肿瘤转移方法.     

Asymmetrically coupled directed percolation systems

We introduce a dynamical model of coupled directed percolation systems with two particle species. The two species A and B are coupled asymmetrically in that A particles branch B particles, whereas B particles prey on A particles. This model may describe epidemic spreading controlled by reactive immunization agents. We study nonequilibrium phase transitions with attention focused on the multicritical point where both species undergo the absorbing phase transition simultaneously. In one dimension, we find that the inhibitory coupling from B to A is irrelevant and the model belongs to the unidirectionally coupled directed percolation class. On the contrary, a mean-field analysis predicts that the inhibitory coupling is relevant and a new universality appears with a variable dynamic exponent. Numerical simulations on small-world networks confirm our predictions.     

Bifurcation analysis of a system of coupled chemical oscillators: Bromate-chlorite-iodine

We examine the dynamical behavior of two chemical oscillators, bromate-iodide and chlorite-iodide, as well as the coupled system bromate-chlorite-iodide. Study of the period and amplitude of oscillation at the bifurcation points yields phase portraits for the uncoupled systems. These are combined to give insights into the nature of the (higher dimensional) coupled system, which exhibits a wide variety of dynamical phenomena, including multiple stationary states, birhythmicity and chaos. Analysis of the topology of the phase portraits and of the experimentally determined return map suggests that the coupled system may possess a Lorenz-type attractor.     

Transverse coupling of chemical waves

The transverse coupling of chemical waves is investigated using a model scheme for excitable media. Chemical waves supported on the surfaces of a semipermeable membrane couple via diffusion through the membrane, resulting in new types of spatiotemporal behavior. The model studies show that spontaneous wave sources may develop from interacting planar waves, giving rise to a complex sequence of patterns accessible only by perturbation. Coupled circular waves result in the spontaneous formation of spiral waves, which subsequently develop patterns in distinct domains with characteristic features. The long time entrainment behavior of coupled spiral waves reveals regions of 1:2 phase locking.     

Cell membrane voltage during electrical cell fusion calculated by re-expansion method

In electrical cell fusion, two cells are first brought into contact by dielectrophoresis, and then a pulsed voltage is applied to induce reversible membrane breakdown at the contact point, by which the membranes of the two cells are reconnected to form a fusant cell. The prediction of the membrane voltage is a crucial issue for high fusion yield, however, its mathematical expression is known only for the case of an isolated cell in a uniform external field. In this paper, we employ the re-expansion method for the transient field analysis of such a multiple cell system. Each cell is modeled by an infinitesimally thin spherical insulating membrane in conducting media, on which accumulation of free charge occurs when an external field is applied. It is shown that the system has two time constants: (a) that governed by the conductivity and the permittivity of the media and (b) that of charging the membrane capacitance through the conducting media, and that the former is far shorter than the latter. Hence, the time variation due to the former is neglected to obtain a simplified expression for the membrane voltage. By expanding the potential into Legendre harmonic components and relating the coefficients for each cell based on the re-expansion method, a differential equation governing the membrane voltage buildup is obtained. The numerical calculation is performed for the axisymmetric case of two cells in contact, to which a step-wise voltage is applied. It is found that the maximum membrane voltage occurs initially at the contact point, but when the steady state is reached, it moves to the ends of the cell pair, and might lead to unsuccessful fusion. The analysis suggests that high-yield fusion may be achieved by an application of shorter pulse, or of a non-uniform field to concentrate the voltage drop at the contact point.     

Chaotic patterns in a coupled oscillator-excitator biochemical cell system

In this paper we examine dynamical modes resulting from diffusion-like interaction of two model biochemical cells. Kinetics in each of the cells is given by the ICC model of calcium ions in the cytosol. Constraints for one of the cells are set so that it is excitable. One of the constraints in the other cell - a fraction of activated cell surface receptors-is varied so that the dynamics in the cell is either excitable or oscillatory or a stable focus. The cells are interacting via mass transfer and dynamics of the coupled system are studied as two parameters are varied-the fraction of activated receptors and the coupling strength. We find that (i) the excitator-excitator interaction does not lead to oscillatory patterns, (ii) the oscillator-excitator interaction leads to alternating phase-locked periodic and quasiperiodic regimes, well known from oscillator-oscillator interactions; torus breaking bifurcation generates chaos when the coupling strength is in an intermediate range, (iii) the focus-excitator interaction generates compound oscillations arranged as period adding sequences alternating with chaotic windows; the transition to chaos is accompanied by period doublings and folding of branches of periodic orbits and is associated with a Shilnikov homoclinic orbit. The nature of spontaneous self-organized oscillations in the focus-excitator range is discussed. (c) 1999 American Institute of Physics.     

Strong phase separation in a model of sedimenting lattices

We study the steady state resulting from instabilities in crystals driven through a dissipative medium, for instance, a colloidal crystal which is steadily sedimenting through a viscous fluid. The problem involves two coupled fields, the density and the tilt; the latter describes the orientation of the mass tensor with respect to the driving field. We map the problem to a one-dimensional lattice model with two coupled species of spins evolving through conserved dynamics. In the steady state of this model each of the two species shows macroscopic phase separation. This phase separation is robust and survives at all temperatures or noise levels- hence the term strong phase separation. This sort of phase separation can be understood in terms of barriers to remixing which grow with system size and result in a logarithmically slow approach to the steady state. In a particular symmetric limit, it is shown that the condition of detailed balance holds with a Hamiltonian which has infinite-ranged interactions, even though the initial model has only local dynamics. The long-ranged character of the interactions is responsible for phase separation, and for the fact that it persists at all temperatures. Possible experimental tests of the phenomenon are discussed.     

Hybrid phase transitions of spreading dynamics in multiplex networks

In this paper, we study the spreading dynamics of social behaviors and focus on heterogenous responses of individuals depending on whether they realize the spreading or not. We model the system with a two-layer multiplex network, in which one layer describes the spreading of social behaviors and the other layer describes the diffusion of the awareness about the spreading. We use the susceptible-infected-susceptible (SIS) model to describe the dynamics of an individual if it is unaware of the spreading of the behavior. While when an individual is aware of the spreading of the social behavior its dynamics will follow the threshold model, in which an individual will adopt a behavior only when the fraction of its neighbors who have adopted the behavior is above a certain threshold. We find that such heterogenous reactions can induce intriguing dynamical properties. The dynamics of the whole network may exhibit hybrid phase transitions with the coexistence of continuous phase transition and bi-stable states. Detailed study of how the diffusion of the awareness influences the spreading dynamics of social behavior is provided. The results are supported by theoretical analysis.     

Entanglement of Non-symmetric Two Charge Qubits Induced by a Damped Cavity

Two charge qubits being coupled to a damped cavity with different couplings are considered. The dynamical evolution of the entanglement between the two qubits is demonstrated analytically or numerically. It is found that with the cavity dissipation, the steady entanglement between the two qubits can be achieved. The two qubits being initially in the separable and most mixed state can be easily induced to a steady entangled state, and the relative difference of the couplings can be used to enhance the steady entanglement between the two charge qubits.     

On the presence of spatial pattern formation in a bistable dynamical system

The aim is to investigate whether in a structural bistable reaction-diffusion system pattern formation may emerge simultaneously from both steady states. Therefore, a dynamical system is modelled by three coupled nonlinear differential equations from which synergetic ordering may arise. In addition, the nonlinear terms are chosen such that the homogeneous system is governed by the canonical form of a cusp bifurcation in a two-dimensional control space. Thus, structural bistability is established. Based on a linear stability analysis the region of bistability is decomposed into four different domains in the control plane. It is shown that in one of these domains self-organization can lead to pattern formation from both steady states simultaneously. In two other domains self-organization can arise from only one steady state and finally in one domain patterning is impossible. An expression for the wavelength of a spatial structure is derived and discussed in terms of parameters of the system. As a possible application of the present results a crystal under irradiation with particles of high energy is considered. It is demonstrated for the case of steel that the parameters of the system can be chosen such that a two-fold spatial instability for irradiation induced cavities may emerge.     

Dissipative solitons with energy and matter flows: Fundamental building blocks for the world of living organisms

We consider a combined model of dissipative solitons that are generated due to the balance between gain and loss of energy as well as to the balance between input and output of matter. The system is governed by the generic complex Ginzburg–Landau equation, which is coupled to a common reaction–diffusion (RD) system. Such a composite dynamical system may describe nerve pulses with a significant part of electromagnetic energy involved. We present examples of such composite dissipative solitons and analyse their internal balances between energy and matter generation and dissipation.